Teaching Physical
Concepts in
Oceanography
An Inquiry-Based Approach
By Lee Karp-Boss, Emmanuel Boss, Herman Weller,
James Loftin, and Jennifer Albright
Contents
Introduction.......................................................................................................................... 1
Chapter 1. Density.............................................................................................................. 4
Encouraging Students to Ask Questions:
A Walk Through a Rich Environment............................................................12
Chapter 2. Pressure..........................................................................................................14
Discrepant Events: Awakening Students’ Curiosity.................................24
Chapter 3. Buoyancy.......................................................................................................25
Assessing Student Learning.................................................................................31
Chapter 4. Heat and Temperature...........................................................................32
Team-Based Learning............................................................................................42
Chapter 5. Gravity Waves.............................................................................................44
Lee Karp-Boss, Emmanuel Boss, and James Loftin are at the School of Marine
Sciences, University of Maine, Orono, ME, USA. Herman Weller and Jennifer
Albright are at the College of Education and Human Development, University
of Maine, Orono, ME, USA. The authors are affiliated with the Center for Ocean
Sciences Education Excellence-Ocean Systems (COSEE-OS), Darling Marine
Center, University of Maine, Walpole, ME, USA.
Support for this project was provided by the National Science Foundation’s
Division of Ocean Sciences Centers for Ocean Sciences Education Excellence
(COSEE), grant number OCE-0528702. Any opinions, findings, conclusions, or
recommendations expressed in this publication do not necessarily reflect the
views of NSF. A pdf of this document is available on The Oceanography Society
Web site at http://www.tos.org/hands_on. Single printed copies are available
upon request from info@tos.org.
©2009 The Oceanography Society
Editors: Ellen Kappel and Vicky Cullen
Layout and design: Johanna Adams
Permission is granted to reprint in whole or in part for any
noncommercial, educational uses. The Oceanography Society requests
that the original source be credited.
INTRODUCTION
material, resulted in the transfer of science facts but did not reflect
the way science is done. In our usual approach, students were
typically passive observers with very little engagement or use of
inquiry. Science, however, is not only about “bodies of knowledge”; science is a way of thinking and doing, where inquiry is an
inherent process. When we “do” science, we make predictions,
generate questions and falsifiable hypotheses, take measurements, make generalizations, and test concepts by application.
According to the National Science Education Standards (National
Research Council, 1996), “In the same way that scientists develop
their knowledge and understanding as they seek answers to questions about the natural world, students develop an understanding
of the natural world when they are actively engaged in scientific
inquiry—alone and with others.” Students do not engage in
inquiry when they are taught about the products of science
(e.g., facts, concepts, principles, laws, and theories) and the techniques used by scientists. In our usual way of teaching science,
labs were often used for science verification. In that mode, the
laws of physics were first introduced and the lab was then used
to illustrate them. Emphasis was on data collection, plotting,
and the writing of reports. Such exercises most often lacked the
element of exploration.
We have come to understand that inquiry and exploration are
essential to exciting students’ curiosity and interest in science.
Outliers in experimental data are often more interesting than the
points that fit theory, as they require an explanation beyond the
material available in textbooks. The explorative approach can
provide students with a deeper understanding of the scientific
process and can help develop critical thinking skills—skills that
are rarely called for in the verification approach.
Our second realization was that a student’s ability to recite
textbook content and formulas does not necessarily indicate an
understanding of the underlying physical principles. Physics can
be taught using mathematical descriptions. Students can learn
which equations will yield which quantities, and this knowledge
can be readily assessed in written exams. However, this approach
does not necessarily develop a student’s ability to recognize
when fundamental principles might be applied to slightly
different problems. We “discovered” that our students achieved
deeper learning and a more profound understanding of physical
concepts when they took an active part in learning—for example,
This supplement to Oceanography magazine focuses on educational approaches to help engage students in learning and offers a
collection of hands-on/minds-on activities for teaching physical
concepts that are fundamental in oceanography. These key
concepts include density, pressure, buoyancy, heat and temperature, and gravity waves. We focus on physical concepts for two
reasons. First, students whose attraction to marine science stems
from an interest in ocean organisms are typically unaware that
physics is fundamental to understanding how the ocean, and all
the organisms that inhabit it, function. Second, existing marine
education and outreach programs tend to emphasize the biological aspects of marine sciences. While many K–12 activities focus
on marine biology, comparatively few have been developed for
teaching about the physical and chemical aspects of the marine
environment (e.g., Ford and Smith, 2000, and a collection of
activities on the Digital Library for Earth System Education Web
site [DLESE; http://www.dlese.org/library/index.jsp]). The ocean
provides an exciting context for science education in general and
physics in particular. Using the ocean as a platform to which
specific physical concepts can be related helps to provide the
environmental relevance that science students are often seeking.
The activities described in this supplement were developed
as part of a Centers for Ocean Sciences Education Excellence
(COSEE) collaboration between scientists and education specialists, and they were implemented in two undergraduate courses
that targeted sophomores, juniors, and seniors (one for marine
science majors and one including both science and education
majors) and in four, week-long workshops for middle- and highschool science teachers. Below, we summarize our educational
approach and discuss the organization of this volume.
Verification or Discovery?
Our approach to teaching science has its basis in three important
“discoveries” we made. We put discoveries in quotation marks
because many people discovered them before us. However, until
we “discovered” them ourselves, we did not realize their significance. This process is similar to the experiences of our students,
who discover for themselves how physics can help explain the
environment in which they live.
Our first realization was that our usual way of teaching science
at the university level, through delivery and recitation of textbook
1
when they performed hands-on experiments that gave them an
opportunity to “see/feel” for themselves what the mathematical
descriptions model.
and learning are occurring. For example, traditional laboratory
exercises, in which students are asked to follow step-by-step,
cookbook-style instructions, can illustrate a scientific principle or
concept, teach students laboratory skills, and provide some handson experience—but they do not provide the “minds-on” aspect of
inquiry. For the “hands-on/minds-on” approach to be successful
in terms of fostering inquiry, students should be encouraged to
ask questions, make predictions and test them, formulate possible
explanations, and apply their knowledge in a variety of contexts.
Students do not enter our classes as blank slates ready to
absorb new information. Rather, they arrive in class with a
diverse set of conceptions (and sometimes misconceptions)
based on their previous experiences. Inquiry-based approaches
allow instructors to probe students’ knowledge and identify
misconceptions that may interfere with learning. Inquiry helps
students understand science as a way of thinking and doing,
encourages them to challenge their assumptions, and creates
an environment in which they seek alternative solutions and
explanations. Broadly applicable skills developed in the inquiry
process—reasoning, problem-solving, and communication—will
be useful to students throughout their lives.
One barrier to our application of an inquiry-based teaching
approach was a concern that this instructional method would
not allow us to cover all the curriculum material within the
prescribed time. This worry is valid, considering our limited
classroom time. We felt, however, that if the purpose of teaching
is to promote meaningful learning experiences in which students
not only gain foundational knowledge but also learn to apply
and integrate concepts, as well as grow towards becoming selfdirected learners, we had to consider an inquiry-based approach.
Given students’ feedback on how beneficial this approach was
to their learning, we came to realize that less is often more. We
advocate for inquiry-based teaching, but we do not believe that
all subject matter should always be taught through inquiry or
that all elements of inquiry (generating questions, gathering
evidence, formulating explanations, applying knowledge to
other situations, and communicating and justifying explanations
[National Research Council, 2000]) must be present at all times.
Effective teaching requires the use of a variety of strategies and
approaches (e.g., Feller and Lotter, 2009) that should be adapted
to the individual classroom, the individual learners, the size and
dynamics of each class, and immediate and long-term learning
objectives, among other factors.
Creating Meaningful
Learning Experiences
Our third realization was that each student has a different set
of predominant learning modalities—that is, some combination
of learning by listening, reading or viewing, touching, or doing
(Dunn and Dunn, 1993). The assumption that “if this teaching
approach worked for me, it must be good for my students” may
not fit all students; after all, we in academia are the minority who
thrived in this educational system. We have “discovered” that
teaching that accommodates a variety of learning modalities
makes our instruction more effective and improves our students’
learning. It was also crucial to become aware that not every
student is a young version of us. Some will simply not possess the
curiosity, interest, and attitudes that motivate scientists. Only
a minority of our students will continue in scientific research.
However, all of them will eventually be consumers of scientific
knowledge, taxpayers who fund our research, and decision
makers in voting booths and public offices. We therefore have a
responsibility to improve our students’ general scientific literacy
and ocean literacy in particular. We need to help them develop
the knowledge and skills required by citizens who will inevitably
face scientific, environmental, and technological challenges.
Inquiry-Based Learning and Teaching
In science teaching, inquiry refers to a way in which learners
become engaged in scientific questions or problems—trying to
solve them by making predictions and testing them, seeking
evidence and information, formulating possible explanations,
evaluating them in light of alternative explanations, and communicating their understanding (National Research Council, 2000).
Inquiry “is far more flexible than the rigid sequence of steps
commonly depicted in textbooks as the ‘scientific method.’ It is
much more than just ‘doing experiments,’ and it is not confined
to laboratories” (AAAS, 1993). There are several models of
inquiry-based teaching and learning (e.g., Hassard, 2005). In our
teaching, we use hands-on/minds-on laboratory activities and
demonstrations, but other effective, inquiry-friendly approaches
that we do not discuss here include the use of case studies,
project-based assignments, and service learning.
We caution that just providing students with laboratory
experiences does not necessarily imply that inquiry teaching
2
How To Use This DOCUMENT
connections to ocean processes are highlighted during the
discussion and through homework assignments.
A 90-minute class period is typically sufficient for students
to complete four to six activities during the first hour, leaving
approximately 30 minutes for group discussion. Note that each
of these activities can stand alone or can be presented as a class
demonstration. Most require simple and affordable equipment
that is generally available in classrooms or homes. We purchased
some equipment at specialized science education stores (e.g.,
sciencekit.com), and we constructed some equipment ourselves.
This document is comprised of five chapters, each focusing
on one of the following physical concepts—density, pressure,
buoyancy, heat and temperature, and gravity waves. For each,
we provide background information followed by detailed
descriptions and explanations of hands-on activities. The activities emphasize different aspects of each concept. This approach
allows students to examine each concept from a variety of
angles, apply what they have learned to new situations, and
challenge their understanding. In addition, we point out several
pedagogical approaches that can improve teaching and foster
learning (see also Feller and Lotter, 2009).
The hands-on activities are presented here in the formats we
use in our college-level classes, which are composed mostly of
sophomore, junior, and senior science and education majors
who have previously taken an introductory oceanography
course. Graduate students and our colleagues also found some
of these activities challenging. For other settings (e.g., students
with different backgrounds) and other curricula, these activities can and should be adapted, with appropriate changes in the
background material, class discussions, activity descriptions, and
explanations. Science teachers who participated in our workshops have successfully adapted some of the activities to their
middle- and high-school classes.
In our classes, activities are most often conducted at classroom
stations through which teams of three to four members rotate. At
times, we present them as a sequence of activities or demonstrations that the class follows collectively, with students seated in
small groups to facilitate discussion. Working in small groups
fosters collaborative thinking and learning. Often, we encourage
a healthy competition among groups (e.g., with group quizzes)
to add a level of excitement and challenge. During class, we
use a Socratic teaching approach in the sense that students are
presented with guiding questions. Students’ questions during the
activities are not always addressed by answers. Rather, we ask
additional questions that lead them to examine their ideas and
views. Students are asked to make predictions, conduct measurements, and find possible explanations for the phenomena they
observe. Once students complete the activities, the class gathers
for a summary discussion during which each group is asked to
offer an explanation for a given activity. Providing students with
time to verbally communicate their views and understanding
is an essential part of our approach. It ensures that misconceptions or difficulties with concepts are identified, discussed,
and ultimately resolved. The applications of a concept and its
References and Other
Recommended Reading
American Association for the Advancement of Science (AAAS). 1993. Benchmarks
for Science Literacy: Project 2061. Oxford University Press, New York,
NY, 448 pp.
Driver, R., A. Squires, P. Rushworth, and V. Wood-Robinson. 1994. Making Sense
of Secondary Science: Research into Children’s Ideas. Routledge, New York,
NY, 224 pp.
Dunn, R., and K. Dunn. 1993. Teaching Secondary Students Through Their Individual
Learning Styles: Practical Approaches for Grades 7–12. Allyn and Bacon, Boston,
MA, 496 pp.
Duschl, R.A. 1990. Restructuring Science Education: The Importance of Theories and
Their Development. Teachers College Press, New York, NY, 155 pp.
Feller, R.J., and C.R. Lotter. 2009. Teaching strategies that hook classroom learners.
Oceanography 22(1):234–237. Available online at: http://tos.org/oceanography/
issues/issue_archive/22_1.html (accessed August 18, 2009).
Ford, B.A., and P.S. Smith. 2000. Project Earth Science: Physical Oceanography.
National Science Teachers Association, Arlington, VA, 220 pp.
Hassard, J. 2005. The Art of Teaching Science: Inquiry and Innovation in Middle
School and High School. Oxford University Press, 476 pp.
Hazen, R.M., and J. Trefil. 2009. Science Matters: Achieving Scientific Literacy.
Anchor Books, New York, NY, 320 pp.
McManus, D.A. 2005. Leaving the Lectern: Cooperative Learning and the
Critical First Days of Students Working in Groups. Anker Publishing
Company Inc., 210 pp.
National Research Council. 1996. National Science Education Standards. National
Academy Press, Washington, DC, 262 pp.
National Research Council. 2000. Inquiry and the National Science Education
Standards: A Guide for Teaching and Learning. National Academy Press,
Washington, DC, 202 pp.
Related Web Sites
• Cooperative Institute for Research in Environmental Science (CIRES):
Resources for Scientists in Partnership with Education (ReSciPE)
http://cires.colorado.edu/education/k12/rescipe/collection/inquirystandards.
html#inquiry
• Perspectives of Hands-On Science Teaching
http://www.ncrel.org/sdrs/areas/issues/content/cntareas/science/eric/eric-toc.htm
• Teaching Science Through Inquiry
http://www.ericdigests.org/1993/inquiry.htm
• Science as Inquiry
http://www2.gsu.edu/~mstjrh/mindsonscience.html
• Science Education Resource Center (SERC), Pedagogy in Action,
Teaching Methods
http://serc.carleton.edu/sp/library/pedagogies.html
3
Chapter 1. DENSITY
PURPOSE OF ACTIVITIES
fluid parcel to increase and its density to decrease (its mass does
not change). Cooling reduces the distance between molecules,
causing the volume of the fluid parcel to decrease and its density
to increase. The relationship between temperature and density
is not linear, and the maximum density of pure water is reached
near 4°C (see Denny, 2007; Garrison, 2007; or any other general
oceanography textbook).
Density is a fundamental property of matter, and although it is
taught in secondary school physical science, not all universitylevel students have a good grasp of the concept. Most students
memorize the definition without giving much attention to its
physical meaning, and many forget it shortly after the exam. In
oceanography, density is used to characterize and follow water
masses as a means to study ocean circulation. Many processes
are caused by or reflect differences in the densities of adjacent
water masses or differences in densities between fluids and
solids. Plate tectonics and ocean basin formation, deep-water
formation and thermohaline circulation, and carbon transport
by particles sinking from surface waters to depth are a few
examples of density-driven processes. The following set of activities is designed to review density, practice density calculations,
and highlight links to oceanic processes.
Density, Stratification, and Mixing
Stratification refers to the arrangement of water masses in layers
according to their densities. Water density increases with depth,
but not at a constant rate. In open ocean regions (with the
exception of polar seas), the water column is generally characterized by three distinct layers: an upper mixed layer (a layer of
warm, less-dense water with temperature constant as a function
of depth), the thermocline (a region in which the temperature decreases and density increases rapidly with increasing
depth), and a deep zone of dense, colder water in which density
increases slowly with depth. Salinity variations in open ocean
regions generally have a smaller effect on density than do
temperature variations. In other words, open-ocean seawater
density is largely controlled by temperature. In contrast, in
coastal regions affected by large riverine input and in polar
regions where ice forms and melts, salinity plays an important
role in determining water density and stratification.
Stratification forms an effective barrier for the exchange of
nutrients and dissolved gases between the top, illuminated surface
layer where phytoplankton can thrive, and the deep, nutrientrich waters. Stratification therefore has important implications
for biological and biogeochemical processes in the ocean. For
example, periods of increased ocean stratification have been
associated with decreases in surface phytoplankton biomass,
most likely due to the suppression of upward nutrient transport
(Behrenfeld et al., 2006; Doney, 2006). In coastal waters, where
the flux of settling organic matter is high, prolonged periods of
stratification can lead to hypoxia (low oxygen), causing mortality
of fish, crabs, and other marine organisms.
Mixing of stratified layers requires work. As an analogy, think
about how hard you need to shake a bottle of salad dressing to
mix the oil and vinegar. Without energetic mixing (e.g., due
to wind or breaking waves), the exchanges of gases and nutrients between surface and deep layers will occur by molecular
BACKGROUND
Density (noted as ρ) is a measure of the compactness of
material—in other words, how much mass is “packed” into a
given space. It is the mass per unit volume ( ρ = m ; units in
V
kg/m3 or g/cm3), a property that is independent of the amount
of material at hand. The density of water is about a thousand
times greater than that of air. The density of water ranges from
998 kg/m3 for freshwater at room temperature (e.g., see http://
www.pg.gda.pl/chem/Dydaktyka/Analityczna/MISC/Water_
density_Pipet_Calibration_Data.pdf) to nearly 1,250 kg/m3 in
salt lakes. The majority of ocean waters have a density range
of 1,020–1,030 kg/m3. The density of seawater is not measured
directly; instead, it is calculated from measurements of water
temperature, salinity, and pressure. Given the small range
of density changes in the ocean, for convenience, seawater’s
density is expressed by the quantity sigma-t (σ t ), which is
defined as σ t = ρ − 1000.
Most of the variability in seawater density is due to changes
in salinity and temperature. A change in salinity reflects a change
in the mass of dissolved salts in a given volume of water. As
salinity increases, due to evaporation or salt rejection during
ice formation, the fluid’s density increases, too. A change in
temperature results in a change in the volume of a parcel of water.
An increase in the temperature of a fluid results in an increase
in the distance between molecules, causing the volume of the
4
DESCRIPTION OF ACTIVITIES
diffusion and local stirring by organisms, which are slow, ineffective modes of transfer (Visser, 2007). The energy needed
for mixing is, at a minimum, the difference in potential energy
between the mixed and stratified fluids. (Some of the energy,
most often the majority, is lost to heat.) Therefore, the more
stratified the water column, the higher the energy needed for
vertical mixing. (Advanced students can be asked to compute
this energy requirement, using the concept that the fluid’s center
of gravity is higher in the mixed fluid relative to the stratified one
[e.g., Denny, 1993]).
Density is fundamentally important to large-scale ocean
circulation. An increase in the density of surface water, through
a decrease in temperature (cooling) or an increase in salinity (ice
formation and evaporation), results in gravitational instability
(i.e., dense water overlying less-dense water) and sinking of
surface waters to depth. Once a sinking water mass reaches a
depth at which its density matches the ambient density, the mass
flows horizontally, along “surfaces” of equal density. This process
of dense-water formation and subsequent sinking is the driver
of thermohaline circulation in the ocean. It is observed in low
latitudes (e.g., the Gulf of Aqaba in the Red Sea, the Gulf of Lions
in the Mediterranean Sea) as well as in high latitudes (e.g., deep
water formation in the North Atlantic). Within the upper mixed
layer, convective mixing occurs due to heat loss from surface
waters (density driven) and due to wind and wave forcing
(mechanically driven).
Density is also fundamentally important to lake processes.
As winter approaches in high latitudes, for example, lake waters
are cooled from the top. As the surface water’s temperature
decreases, its density increases, and when the upper waters
become denser than the waters below, they sink. The warmer,
less-dense water underneath the surface layer then upwells to
replace the sinking water. If low air temperatures persist, these
cooling and convective processes will eventually cool the entire
lake to 4°C (the temperature of maximum density for freshwater
at sea level). With yet further surface cooling, the density of the
upper waters will decrease. The lake then becomes stably stratified, with denser water at the bottom and colder but less-dense
water above. When surface waters further cool to 0°C, they begin
to freeze. With continued cooling, the frozen layer deepens.
Activities 1.1–1.3 are used to review density, and Activities
1.4–1.6 highlight links to oceanic processes. Activities 1.1–1.3
emphasize the relationship between an object’s mass, volume,
and density and its sinking or floating behavior. These
activities also allow students to practice measurement skills.
Measurements and related concepts such as precision and
accuracy, and statistical concepts such as average and standard
deviation, can be introduced during class and/or provided as
homework. In Activities 1.4–1.6, students examine relationships
among density, stratification, and mixing, and then discuss
applications to ocean processes.
Activities are set up at stations prior to class (typically four
to five stations per 90-minute class period, with the choice of
activities, level of difficulty, and depth of discussion dependent
on the students’ backgrounds). Students are asked to rotate
among stations to complete the assignments. During this time,
instructors move among the groups and guide students by asking
probing questions. The last ~ 30 minutes of class are used for
summary and discussion.
Activity 1.1. Will It Float? (Figure 1.1)
Materials
•
Two solid, approximately equal-volume wooden
cubes, one made of balsa and the other of lignum vitae
(from sciencekit.com)
• Large, hollow metal ball (from sciencekit.com)
Figure 1.1. Materials for Activity 1.1.
5
We discuss the commonly used phrase “heavy things sink, light
things float” and point out the potential misconception that
could arise. (2) The floating or sinking behavior of an object does
not depend only on the material from which the object is made
(e.g., addressing the common misconception that wood always
floats). If time allows, a discussion on volume measurements
(based on measured dimensions or volume displacement) can be
brought in, leading to the concept of buoyancy, which is introduced in Chapter 3.
•
Small Delrin ball or other solid plastic sphere (available
at any hardware store)
• Container filled with room-temperature tap water
• Ruler or caliper
• Balance
Instructions to the Students
1. Make a list of properties that you think determine whether an
object sinks or floats.
2. Feel the objects provided and predict which will float in
water and which will sink. What is the reasoning behind your
prediction? Discuss your prediction with your group.
3. Test your prediction. Do your observations support your
prediction? If not, how can you explain it?
4. Based on your observations, how would you revise your list of
properties from Step 1?
5. Determine the mass and volume for each cube and ball. Can
you suggest more than one method to obtain the volumes
of the cubes and balls? (If time allows: How do the densities
obtained by the different methods compare?)
6. What is the relationship, if any, between the masses of the
objects and the sinking/floating behaviors you observed?
What is the relationship, if any, between the volumes of the
objects and the sinking/floating behaviors you observed?
7. Calculate the densities of the cubes, balls, and tap water. What
is the relationship, if any, between the densities you calculated
and the sinking/floating behaviors you observed?
Activity 1.2. Can a Can Float? (Figure 1.2)
Materials
•
•
•
•
•
A can of Mountain Dew and a can of Diet Mountain Dew
Large container filled with room-temperature tap water
Caliper or ruler
Balance
2-liter graduated cylinder
Instructions to the Students
1. Examine the two cans. List similarities and differences
between them.
2. What do you think the floating/sinking behavior of each can
will be when placed in room-temperature tap water? Write the
reasoning for your prediction.
3. Place the two cans in the tank. Be sure no bubbles cling to the
cans. Does your observation agree with your prediction? How
would you explain this observation?
4. How would you determine the density of each can? Try your
approach. How do the densities of the cans compare to the
density of tap water?
5. Are your density measurements in agreement with your observations? Why might there be a difference in density between
the cans and/or between the cans and the water?
Explanation
In this activity, students experiment with four objects—two
types of solid wooden cubes, a hollow metal ball, and a solid
plastic sphere. We use two types of wood that differ greatly
in density: balsa, with a density range of 0.1–0.17 g/cm3 (the
specific cube we use has a mass of 2.25 g and a volume of
16.7 cm3, hence a density of 0.13 g/cm3), and lignum vitae, with
a density range of 1.17–1.29 g/cm3 (the specific cube we use
has a mass of 19.6 g and a volume of 15.2 cm3, hence a density
of 1.29 g/cm3). The densities of the small plastic ball and the
larger hollow metal ball are 1.4 g/cm3 (mass of 1.5 g and volume
of 1.07 cm3) and 0.14 g/cm3 (mass of 144 g and volume of
1035 cm3), respectively. Because the density of tap water at room
temperature is ~ 1 g/cm3, the balsa cube and the metal ball will
float, and the lignum vitae cube and the plastic ball will sink.
This activity illustrates two key points: (1) The floating or
sinking behavior of an object does not depend on its mass or
volume alone but on the ratio between them—that is, its density.
Figure 1.2. Difference in densities and, hence, sinking and floating behaviors
between a can of ordinary soda (right) and a can of diet soda (left).
6
Explanation
When students place the two cans in a tub of freshwater, the
can of ordinary soda sinks and the can of diet soda floats
(Figure 1.2). Calculated densities of the cans of Mountain
Dew and Diet Mountain Dew that we use (including the can,
liquid, and gas) are 1.024 g/cm3 and 0.998 g/cm3, respectively.
The difference in density is due to differences in the mass of
sweeteners added to the regular and diet cans. A can of ordinary Mountain Dew contains 46 g of sugar! It will leave a big
impression on your students if you weigh out 46 g of sugar to
demonstrate the amount of added sugar (see right hand side
of Figure 1.2). Variations of this activity are available on the
Internet. We caution that variability exists among different
brands of soda and among cans within the same brand; in
some cases, both diet and regular soda cans will float (or
sink). Instructors should always test the cans before class.
Alternatively, a case in which a can that is supposed to float
does not can be turned into a teachable moment where students
are challenged to test their understanding. This activity is an
example of a discrepant event (see discussion on p. 24). Because
the cans look and feel similar, students do not expect them to
be different in terms of their sinking and floating behaviors.
During the activity, students often raise the question of how to
measure the volume of the cans (by volume displacement or by
measuring dimensions of the can and calculating the volume
of a cylinder). We let them choose an approach and since
each group uses the same cans, we compare density estimates
obtained by each. If time allows, we ask each group to use both
approaches and compare their density estimations. One could
further develop this activity to include estimates of the precision
of each approach, as well as discussions on measurement accuracy and error propagation.
Figure 1.3. Materials for Activity 1.3.
Instructions to the Students
1. Determine the densities of the two rock samples. How do the
densities of granite and basalt compare?
2. The average elevation of land above sea level is 875 m. The
average depth of the ocean floor is 3,794 m below sea level.
Apply your density calculations and your previous knowledge
about Earth’s structure to explain this large difference in elevation between continents and ocean basins.
3. Textbook values of oceanic crust and continental crust are
2.9–3.0 g/cm3 and 2.7–2.8 g/cm3, respectively. How do these
values compare to your measurements? If they differ, what
may account for the differences between the values you
obtained and those given in textbooks?
4. Given that Earth’s mass is 5.9742 x 1024 kg and that Earth’s
radius is 6,378 km, calculate the density of the planet.
(Challenge: How would one determine Earth’s mass?). How
does Earth’s density compare to the density of the rocks? What
does this tell you about Earth’s structure?
Activity 1.3. Densities of Oceanic
and Continental Crusts (Figure 1.3)
Explanation
The densities of rock samples we use are 2.8 g/cm3 for basalt
(oceanic crust origin) and 2.6 g /cm3 for granite (continental
crust origin). Both types of crust overlie Earth’s denser mantle
(3.3–5.7 g/cm3). Continental crust is thicker and less dense than
the depth-averaged oceanic crust plus the overlying water and
therefore floats higher on the mantle than does oceanic crust.
During the activity and the subsequent class discussion, we
highlight three issues. The first concerns volume measurements
of irregular shapes by water displacement. This concept is later
linked to a follow-up lesson on buoyancy (Chapter 3). Next, we
discuss the issue of measurements and variability associated with
This activity has been modified after one designed by
Donald F. Collins, Warren-Wilson College.
Materials
•
Rock samples of basalt (representative of oceanic crust) and
granite (representative of continental crust)
• An overflow container with a spout and a 50-ml graduated
cylinder to catch displaced water (alternatively, a large graduated cylinder or a container with gradation lines will work)
•
Balance
7
measurements. Science students are accustomed to seeing textbook values of quantities that represent averages, often without
any statistical information on the associated uncertainties or
natural variance. Furthermore, some students believe that if you
don’t get the exact value provided in a textbook, you are wrong.
At the end of the class, we compare the groups’ density measurements and their methods, and then discuss potential sources of
variability in measurements and what it is that textbook values
actually represent. (Statistical concepts of averages and standard deviations can also be brought in here.) Last, we highlight
applications—how differences in the densities and thicknesses of
continental and oceanic crusts shape Earth’s topography, as well
as their relation to plate tectonic processes. For a derivation of
Earth’s average mass and density, see Box 1.1.
Figure 1.4. Tank before (top) and after removal of divider (bottom).
ACTIVITY 1.4. Effects of Temperature
and Salinity on Density and
Stratification (Figure 1.4)
Instructions to the Students
1. Fill a beaker with tap water.
2. Place water from the beaker in one compartment of the tank
and water from the salt-solution bottle in the other. Add a few
drops of one food coloring to one compartment and a few
drops of the other food coloring to the other compartment.
What do you predict will happen when you remove the divider
between the compartments? Explain your reasoning.
3. Measure the densities of the room-temperature tap water and
the salt solution.
4. Test your prediction by removing the tank divider. What
happens? Are your observations consistent with the densities
you measured?
Materials
•
•
•
•
•
Rectangular tank with a divider (from sciencekit.com)
Bottle containing pre-made salt solution (approximately
75 g salt dissolved in 1 L water: kosher salt yields a clear solution while a solution made with table salt, at high concentrations, appears milky)
Food coloring (two different colors)
Ice
Beakers
Box 1.1. Obtaining the Mass and Density of Planet Earth
Earth’s mass can be computed from Newton’s laws:
1. Newton’s Law of Universal Gravitation states that the force (attractive force) that two bodies exert on each other is directly
proportional to the product of their masses (m1, m2) and inversely proportional to the square of the distance between them (L):
F = Gm1m2 /L2, where G is the gravitational constant (G = 6.7 x 10-11N m2/kg2). If we assume that the body is near Earth’s
surface, then the planet’s radius can be used as the distance between the body and Earth.
2. Newton’s Second Law states that the force attracting a body to Earth equals its mass (m) times the gravitational acceleration (g):
F = mg, where, for Earth’s surface, g = 980 cm /s2 (g itself can be computed, for example, from the period of a pendulum).
Let m1 be Earth’s mass and m2 be a body’s mass:
F = m2 g = Gm1m2 /L2 . Earth’s mass is therefore m1 = g L2/G ≈ 6 x 10 24 kg. Dividing by Earth’s volume (4/3πr 3, where r is Earth’s
radius; here we used an average of 6,373 km), we obtain Earth’s density (5,515 kg/m3 or 5.515 g/cm3).
8
Instructions to the Students
5. Empty the tank and fill one beaker with hot tap water and one
beaker with ice-cold water. Add a few drops of food coloring
to each of the beakers (different color to each beaker).
6. Place the hot water in one tank compartment and the icecold water in the other. Repeat Steps 3–5. After removing the
divider and observing the new equilibrium in the tank, place
your fingertips on top of the fluid surface and slowly move
your hand down toward the bottom of the tank. Can you feel
the temperature change?
7. How might the effects of climate change, such as warming
and melting of sea ice, affect the vertical structure of the water
column? Discuss possible scenarios with your group (alternatively, this question can be given as a homework assignment).
1. Predict in which tank a dye introduced at the surface will mix
more easily throughout the tank.
2. In the tank with the nonstratified water column, use a long
pipette to carefully inject a few drops of food coloring at
the water’s surface. Using the hair dryer, generate a “wind”
flowing roughly parallel to the fluid’s surface, and observe how
the dye mixes.
3. With the tank containing the two-layer fluid, use the long
pipette to carefully inject a few drops of food coloring at the
water’s surface and a few drops of a different food coloring at
the bottom of the tank. Using the hair dryer, generate a wind
similar to the one you generated in Step 2. Compare your
observations to what you saw happen in the nonstratified tank.
4. In light of your observations, predict and discuss with your
group some potential effects of global warming on stratification and mixing in the ocean and in lakes. What might be
some consequences for marine organisms?
Explanation
This activity demonstrates that fluids arrange into layers
according to their densities. The two “water masses”
(Figure 1.4)—salt (blue) vs. fresh (yellow), or cold (blue) vs.
warm (yellow)—are initially separated by the tank’s divider.
When the divider is removed, the denser water (salt water or
cold water [blue]) sinks to the bottom of the container and the
less-dense water (fresh or warm water [yellow]) floats above,
forming a stratified column. In the process, an internal wave
is formed in the tank (which we discuss in more detail in
Chapter 5, Gravity Waves).
Explanation
In the nonstratified water column (Figure 1.5, left panel), red dye
added at the fluid’s surface initially sinks because its density is
slightly higher than that of the water (Figure 1.5, top left). After
a short time of exposure to a stress on the surface (“wind” generated by a hair dryer), the dye mixes throughout the water column
(Figure 1.5, bottom left). In the stratified tank (right panel),
the pycnocline, the region of sharp density change between the
layers, forms an effective barrier to mixing (Figure 1.5, top right).
More energy is required to mix the two layers, and the “wind”
generated by the hair dryer is no longer sufficient to mix the
entire water column. As a result, the red dye mixes only within
Activity 1.5. Effect of
Stratification on Mixing (Figure 1.5)
This activity is based on a demonstration communicated to us by
Peter Franks, University of California, San Diego. See Franks and
Franks (2009) for details of that physical simulation.
Materials
•
Tank containing tap water
Tank containing stratified fluid*
• Hair dryer
• Food coloring (two different colors)
• Long pipettes
*To prepare a tank with a two-layer stratified fluid, fill half
to three-quarters of the tank with a strong saltwater solution (see Activity 1.4). Place a piece of thin foam (same width
as the tank) over the water, and carefully pour warm tap
water over the foam. Then remove the foam piece carefully,
without stirring and mixing the fluids. For another technique,
see Franks and Franks (2009).
•
Figure 1.5. Tanks with dye before (top) and after (bottom) application of
mechanical forcing (blowing of a air dryer parallel to top). Left side: nonstratified tank, right side: density-stratified tank.
9
Explanation
the upper layer, analogous to the upper mixed layer in oceans
and lakes (Figure 1.5, bottom right). Calculations of the energy
required to increase the depth of the pycnocline by mixing,
raising the center of gravity of the fluid, can be used in conjunction with this activity (e.g., Denny, 2007).
Figure 1.6, left panel: In tap water, the ice block floats because
the density of ice is lower than that of freshwater. As the ice
melts, however, cold, colored meltwater sinks to the bottom
because it is denser than the tap water. Warmer water from the
bottom is then displaced and upwells, resulting in a convective
flow visible in the dye patterns. Ice melting in the center of the
tank is analogous to a convection “chimney” formed in the
open ocean, while ice melting at the tank’s edge is analogous
to a chimney on a continental shelf (near a land mass). Such
chimneys in the ocean, created and sustained by convective
processes, appear as “columns” of mixed water that flow
downwards. For a given set of oceanic and meteorological
conditions, open-water convection tends to entrain (mix with)
more of the surrounding waters than does convection near a
land mass. The open-ocean case therefore results in downwelled
water that is less dense.
Figure 1.6, right panel: The ice block is floating in dense, salty
water. As the ice melts, only a small amount of dye sinks because
the density of the saltwater is greater than the density of the
newly melted, fresh, ice-cold water. Most of the meltwater accumulates in a surface layer on top of the denser salt layer.
Activity 1.6. Convection Under Ice
(Figure 1.6)
Materials
•
At least four blocks of colored ice (add food coloring to water,
then freeze in food-storage containers)
• Two large transparent containers—one filled with tap water
and one filled with saltwater (both at room temperature)*
*It is necessary to replace water in the containers each time a
new group of students arrives at the station. As ice melts, the
color mixes with water and after a while it becomes difficult to
observe the pattern of flow.
Instructions to the Students
1. Place a block of colored ice in the container filled with tap
water. As the ice melts, observe and explain the behavior
of the fluids.
2. Place the other block of colored ice in the container filled with
saltwater. As the ice melts, observe and explain the behavior
of the fluids. Compare these observations with what you
saw in Step 1.
Note to instructor: Advanced students can be asked to
observe whether the fluids’ behavior in the tanks depends
on whether the ice is near the tank walls or at the center
of the tank and relate these observations to likely oceanic
scenarios (e.g., convection chimneys in the open ocean vs.
convection on a shelf).
Supplementary Activity (Figure 1.7)
Time permitting, students’ understanding of the concept of
density can be assessed at the end of the lesson by giving them
a Galileo thermometer (Figure 1.7; inexpensive and available
online), a container with hot water, and a container with cold
water, and asking them to explain how the thermometer works.
A Galileo thermometer is made of a sealed glass tube containing
a clear fluid and calibrated, fluid-containing glass balls with
metal tags attached to them. The balls, each having a slightly
different density, are all suspended in the clear fluid. They are
sealed and therefore each has a constant volume and mass,
hence, constant density. What changes as a result of heating or
cooling is the density of the surrounding fluid. The change in
relative density between the glass balls and the clear fluid causes
the balls to rise or sink and rearrange according to their equilibrium densities. Usually the balls separate into two groups,
one near the bottom and one near the top of the column.
Temperature is then read from metal disks attached to the balls:
the reading on the disk of the lowermost ball of the group near
the top of the column indicates the temperature. We caution
that it takes a long time for a Galileo thermometer to register
changes in temperature after being switched from a warm water
bath to a cold water bath (or vice versa), due to the slow rate
Figure 1.6. Convection associated with melting of a colored ice block in tap
water (left) and saltwater (right).
10
Figure 1.7. A Galileo thermometer.
at which the internal liquid changes temperature. This slow
equilibration is especially pronounced when the thermometer
is placed in an ice bath, because the cold (dense) liquid remains
near the bottom. Periodically tilting the thermometer can
reduce the wait time. For a short-term demonstration, it is better
to compare two thermometers, one placed in a warm water bath
and one placed in a cold water bath.
References
Behrenfeld, M.J., R. O’Malley, D.Siegel, C. McClain, J. Sarmiento, G. Feldman,
A. Milligan, P. Falkowski, R. Letelier, and E. Boss. 2006. Climate-driven trends
in contemporary ocean productivity. Nature 444:752–755.
Denny, M.W. 1993. Air and Water: The Biology and Physics of Life’s Media. Princeton
University Press, Princeton, NJ, 360 pp.
Denny, M. 2007. How the Ocean Works: An Introduction to Oceanography. Princeton
University Press, Princeton, NJ, 344 pp.
Doney, S. 2006. Plankton in a warmer world. Nature 444:695–696.
Franks, P.J.S., and S.E.R. Franks. 2009. Mix it up, mix it down: Intriguing implications of ocean layering. Oceanography 22(1):228–233. Available online at:
http://www.tos.org/hands-on/index.html (accessed August 4, 2009).
Garrison, T.S. 2007. Oceanography: An Invitation to Marine Science. Sixth edition.
Thomson Brooks/Cole, 608 pp.
Visser, A. 2007. Biomixing of the oceans? Science 316:838.
Other Resources
http://cosee.umaine.edu/cfuser/index.cfm. This COSEE-OS ocean-climate
Web site provides images of density profiles and thermohaline circulation,
videos on ocean convection, a collection of hands-on activities, and links
to related concepts.
Ford, B.A., and P.S. Smith. 2000. Project Earth Science: Physical Oceanography.
National Science Teachers Association, Arlington, VA, 220 pp.
11
Encouraging Students To Ask Questions:
A Walk Through a Rich Environment
B ased on W elle r , 1 9 8 8
Questioning is an integral part of science inquiry (National
Research Council, 2000) and holds many educational merits.
The National Research Council (2000, p. 29) describes a
learner’s engaging in “scientifically oriented questions” as one
of the five essential features of classroom inquiry. Students’
questions may reveal much about their understanding and
reasoning, and uncover alternative frameworks and misconceptions. Students’ asking of questions can stimulate their
curiosity and motivation, help them develop critical and
independent thinking skills, and make them active participants. However, in a typical lecture, students seldom ask
questions; questioning is done primarily by the instructor.
When senior undergraduates in our program were asked why
they rarely asked questions in class, the two most common
answers were: (1) a fear of appearing stupid, and (2) a class
atmosphere not conducive to asking questions. Many students
commented that their formal educational experiences had
led them to develop the notion that their expected role as
learners was to be present in class, take notes, and complete
homework assignments and exams. The skill of asking
questions was not one that had been emphasized as part of
their formal education.
We describe here an approach we use to encourage students
to ask questions.
In the first class period of a course, we take the students on
a walk through a rich, stimulating environment. The purpose
of the walk is to expose them to an object-rich environment
that will incite spontaneous questions. This approach is derived
from a parallel elementary-school approach intended to elicit
questions from young students (Jelly, 2001).
For the rich environment, we use the University of Maine
aquaculture facility, where tropical fish are raised for research
and commercial purposes. We do not tell students anything
about the environment prior to the walk. We instruct them
only to write down questions that come to mind as they
explore the environment, focusing on questions that truly
interest them (rather than questions one might find in a
12
textbook). After about 30 minutes of unconstrained exploration, each student is asked to choose three to five favorite
questions from his/her list to contribute to a class list. The
class list can be compiled electronically or manually using
white boards or flip charts, allowing students to visually
appreciate the quantity, quality, and diversity of the questions
they generated. Examples of students’ questions during the
aquaculture walk include: “Do fish play?” “Do algae promote
or inhibit spawning?” “How do you transport the tropical fish
in extreme weather conditions, and what is their mortality
rate in the process?”
Next, we ask students to form teams, and each team is
asked to categorize the questions based on similar characteristics. A representative from each team explains to the class
the reasoning for the choice of categories. These cooperative
learning techniques of classroom organization encourage
all the students to carefully consider all the questions, and
eliminate the “blurting out” of categories by a small number
of students. For example, in 2007, the categories developed
by the three small groups were: Group A—biology, facility,
environment, business; Group B—environment, life cycle of
fish, facility/marketing; and Group C—exploratory, biology/
ecosystem, technical, facility/economics. This activity may be
the first time that some of the students have categorized raw
data without any instructor hints.
For closure, we ask the students to share their views on how
their walk, questioning, and categorization might resemble
what scientists do in the initial exploratory phase of a research
undertaking. We also ask students to describe what they
believe makes a question a good science question. We discuss
this topic as a class, referring to questions they generated,
to illustrate characteristics of good science questions. The
students often respond that a good science question should
be as specific as possible and not involve nonscience aspects
of belief, politics, and ethics. Additional aspects that we bring
up during the discussion include: A good science question
should (1) be as specific as possible, isolating the essentials of a
problem; (2) not “assume an answer” (Sagan, 1996), but create
falsifiable, alternative hypotheses as to what are answers to the
question; (3) not involve pseudoscience (Derry, 1999; Sagan,
1996); and (4) not involve something we cannot acquire information about (Sagan, 1996). For deeper discussions of these
aspects of scientific questioning, we recommend Derry (1999),
Sagan (1996, Chapter 12, pages 201–218), and Atkins (2003,
pages 3–4). Finally, we discuss the power of questioning in
learning and ask students to share their feelings about asking
questions in class. We use this opportunity to remind students
that questioning will be an integral part of the class.
This exercise sets the tone for our course, increases students’
comfort with asking questions, and ultimately enhances
student learning. As extensions of this approach, students
could be asked to seek answers for their own questions as a
homework or term-paper assignment. The exercise could also
be used in the middle of a course to capture students’ interest
when a new topic is introduced. Note that a rich environment
does not have to be a specialized facility. Class demonstrations,
video clips, computer simulations, and/or photos and images
could readily serve to stimulate students’ questioning.
References
Atkins, P. 2003. Galileo’s Finger: The Ten Great Ideas of Science. Oxford University
Press, 400 pp.
Derry, G.N. 1999. What Science Is and How It Works. Princeton University Press,
Princeton, NJ, 328 pp.
Jelly, S. 2001. Helping children raise questions—and answering them. Pp. 36–47
in Primary Science: Taking the Plunge. W. Harlen, ed, Heinemann,
London, UK.
National Research Council. 2000. Inquiry and the National Science Education
Standards: A Guide for Teaching and Learning. National Academy Press,
Washington, DC, 202 pp.
Sagan, C. 1996. The Demon-Haunted World: Science as a Candle in the Dark.
Ballantine Books, New York, NY, 480 pp.
Weller, H.G. 1998. A running inquiry—Nature asked the questions during this
jog. Journal of College Science Teaching 27:389–392.
13
Chapter 2. PRESSURE
PURPOSE OF ACTIVITIES
Although students may not realize it, pressure varies from
place to place, both in the ocean and in the atmosphere. Spatial
variations in pressure are the driving force for ocean currents
and winds. For example, the trade winds blow from the normally
stable high-pressure area over the eastern Pacific to the lowpressure area over the western Pacific. However, for reasons
that are not yet fully understood, these pressure patterns shift
every three to eight years, causing the trade winds to weaken
and then reverse direction. This change in atmospheric pressure
is called the Southern Oscillation. Equatorial Pacific changes
in ocean circulation associated with the Southern Oscillation
result in the phenomenon known as El Niño, which has serious
global consequences.
Pressure in the ocean increases nearly linearly with depth.
Different marine organisms are adapted to life at a particular
depth range. Gas-filled cavities within animals and other organisms are compressed under pressure (see below). Additionally,
the solubility of gases is affected by pressure, with important
consequences for the diving physiology of both humans and
marine organisms. Pressure not only puts constraints on marine
organisms, but they can also use it. For example, pressure changes
associated with the flow of water over mounds and other protrusions enhance the flow’s velocity, and thus the delivery of food to
suspension feeders (e.g., barnacles), and oxygenated water into the
burrows of sediment-dwelling organisms (see below).
This set of activities is intended to help students understand
the concept of pressure in fluids. Teaching about pressure
through its mathematical expressions (i.e., the hydrostatic equation, Bernoulli’s equation) may not reach less mathematically
oriented students. Thus, we use a series of activities that allows
students to examine pressure from different angles. We begin
by revisiting the physical definition of pressure and introducing
examples from everyday life. This structure provides students
with a familiar entry point into an often poorly understood
concept and helps motivate students by making learning more
relevant. Then, through hands-on, inquiry-based activities, we
illustrate the concepts of hydrostatic pressure, compressibility of
gases under pressure (i.e., Boyle’s Law), and pressure in moving
fluids (i.e., Bernoulli’s Principle). We highlight the significance
of these principles to processes in the ocean, from ocean circulation to the evolution of adaptations commonly found in marine
organisms today.
BACKGROUND
Pressure (P) is defined as the force (F) applied on a unit area (A)
in a direction perpendicular to that area:
P= F.
A
Thus, pressure depends on the area over which a given force
is distributed. Pressure is a scalar, and hence has no directionality. A directional force from high to low pressure is
applied on an object when the pressure varies across an object.
The commonly used unit of pressure is Pascal (Pa), where
1 Pa = 1 N/m2 = kg/m·s2 (N = Newton). Units such as pounds per
square inch (psi), bar, and standard atmosphere (atm) are also
used in oceanic and atmospheric applications.
Many phenomena encountered daily are associated with
the concept of pressure. Among them are wind, differences in
the performances of a sharp vs. a blunt chopping knife or axe,
and drinking with a straw. Atmospheric pressure at sea level
has a magnitude of nearly 105 Pa. Our bodies do not collapse
as a result of this pressure because no net force is applied on
them (an equal pressure exists within the body). Our senses do
not detect absolute pressure, but do detect change in pressure
(e.g., a change in pressure that is generated within gas-filled cavities when we dive or fly).
Hydrostatic Pressure (Fluids at Rest)
The pressure at a given depth in the ocean is a result of the force
(weight) exerted by both the water column and air column above
it. This pressure, in fluids at rest, is termed “static pressure” or
“hydrostatic pressure.” Hydrostatic pressure (Ph) is a function of
the density of a fluid and the height of the fluid column (depth).
The relationship is defined by the hydrostatic equation P = ρgz,
where ρ is the depth-averaged density, g the gravitational acceleration, and z the height of the water column (see Box 2.1 for
the derivation). The hydrostatic equation is central to studies
of ocean circulation. For example, geostrophic currents (such
as ocean gyres and Gulf Stream rings) are determined by the
balance between horizontal pressure gradients and the Coriolis
acceleration (an acceleration resulting from Earth’s rotation).
Differences in hydrostatic pressure between two locations result
in a force per unit volume exerted on the fluid (air or water)
14
Box 2.1. Calculating Hydrostatic Pressure
Assume a water column with a cross-sectional area, A, and a depth (height), z. The volume of the water column is Az. The
force that this column exerts on a given cross section is F = weight = mg, where m is the mass of water above the cross section
and g is gravitational acceleration. The mass can be conveniently expressed in terms of the density (here assumed constant)
and the volume of the water: m = ρV. Thus, F = ρVg. The force per unit area (the pressure, P) is, therefore,
P = ρVg/A = ρ(Az)g/A = ρgz. If density varies with depth (a change usually smaller than 1% in the ocean), the depth-averaged
density is used instead of density (calculated by integrating density with respect to depth and dividing by the water column’s
depth). When measuring pressure in fluids, the hydrostatic equation comes in very handy. Devices such as manometers
(Activity 2.4) are used to measure pressure relative to a reference pressure (usually atmospheric pressure).
Two other important points should be mentioned with respect
to hydrostatic pressure. The first is the transmission of pressure
through the fluid. Pressure that is applied to one part of a fluid
is transmitted throughout the entire fluid (known as Pascal’s
Principle). Information about the occurrence of a pressure
change within the fluid propagates by sound waves at the speed
of sound (~ 1,500 m/s), which in our laboratory setups (e.g., a
Cartesian diver in Chapter 3) seems instantaneous. If you take a
balloon full of water and submerge it under water, the hydrostatic
pressure outside the balloon equals the pressure inside it and the
balloon maintains its shape and size. This principle is the reason
why you don’t feel pressure on your body (except for air cavities;
see below) when you dive. Transmission of pressure by fluids is
the principle used in hydraulic devices (e.g., car lifts in service
stations, hydraulic jacks, construction machines that are used for
lifting heavy loads).
acting from the region of high pressure to the region of low pressure. Because of Earth’s rotation, the resulting fluid motion is not
“downhill” from high to low pressure (as the fluid would do in
a nonrotating environment), but rather along lines of constant
pressure. At the equator, however, where the Coriolis effect is
small, winds and currents are mostly down pressure gradients.
It is impractical to reliably measure horizontal changes in pressure along surfaces of fixed depths in the ocean because pressure
and depth are scaled versions of the same vertical coordinate (to
a first order). Instead, oceanographers use the dynamic height
method in which two equal pressure reference points are chosen
and the depth-integrated densities of the water columns above
these reference points are calculated and compared. It is assumed
that these two reference points are located on an isobaric
“surface” (an imaginary surface where pressure is the same everywhere), and therefore there is no horizontal water motion at that
chosen depth. If ρ1 ≠ ρ2 (where ρ1 and ρ2 are the depth-integrated
densities at reference points 1 and 2, respectively), then z1 and z2
(the heights of the water column above reference points 1 and 2)
must be different. Differences in the heights of the water column
above the reference depth are used to calculate sea surface slopes;
for example, across the Gulf Stream (about 70-km wide), the
surface height drops more than 1 m. The calculated slope is
proportional to the pressure gradient that is required for estimations of geostrophic currents’ speeds (e.g., Figure 10.7 at http://
oceanworld.tamu.edu/resources/ocng_textbook/chapter10/
chapter10_04.htm). Today, it is possible to determine sea-surface
slopes using satellite altimetry.
Compressibility of Gases Under Pressure
In the ocean, pressure increases at a rate of 1 atm (105 Pa) per
10 m. Organisms that live or dive to great depths are therefore
subjected to high compression forces due to the weight of the
water column above them. One of the primary differences
between water and gases is that water is a highly incompressible
fluid and gases are compressible. The volume of a fixed amount
of gas is inversely proportional to the pressure within it (known
as Boyle’s Law); if the pressure doubles, the volume of the gas
shrinks by half. Because the human body is comprised mostly of
water, it does not compress significantly when diving in water.
15
Pressure is only felt in sealed air cavities such as sinuses, ears,
and lungs. This is why a person’s ears may hurt when diving
only a few meters deep in a pool. Marine mammals that dive to
great depths have developed adaptations to overcome potential
damage to air cavities such as lungs. Conversely, Boyle’s Law
also illustrates the danger of expanding gases when pressure
is reduced by moving to shallower depths. When a scuba diver
breathes compressed air at a depth of 10 m (where the total
pressure is 2 atm) and then ascends to the surface while holding
his/her breath, the air in the lungs will try to expand to twice
the volume. Some air must be released or the lungs may rupture.
Similar damage would occur to the gas bladders of many species
of fish if they ascended too rapidly. Therefore, some species of
bottom-dwelling fish are restricted in their vertical movement,
and may be killed when hauled up by fishing gear. Other species
have evolved pathways to rapidly vent their gas bladders and are
therefore not restricted in their vertical movements.
In the discussion above, we assumed temperature to be
constant. It may be useful to ask students how changes in
temperature might affect changes in volume of a submerged
object. The Ideal Gas Law states that for a given volume of gas,
pressure increases with temperature (discussion of molecular
kinetic energy will fit well here). However, in the ocean, the
change of temperature with depth has a much smaller range
(about 10% in Kelvin units through the full ocean depth) than
the change of pressure with depth (1 atm every 10 m). Thus,
volume changes of gas-filled cavities as a function of depth are
dominated by pressure.
Accelerating Fluids: Bernoulli’s Principle
When the velocity of a fluid changes along its path, simultaneous changes in pressure are at play. The relationship between
fluid pressure and its velocity, known as Bernoulli’s Principle
(Box 2.2), can be derived from the principle of conservation of
energy or from Newton’s Second Law (F = ma). Many organisms, such as sponges, ascidians, and other suspension feeders,
appear to take advantage of the flow of surrounding water to
supplement their pumping activity (Vogel, 1978). For example,
the burrowing shrimp Callianassa filholi builds large mounds
surrounding an opening to the outside. Similar to a house
chimney, the flow passing over the mound has to accelerate
(accommodating a smaller cross section); coincident with this
acceleration is a lower pressure above the opening, creating an
updraft within the ventilation tube.
DESCRIPTION OF ACTIVITIES
We often begin the discussion of pressure by showing an image
of a ballerina standing on one foot and an elephant standing on
Box 2.2. Bernoulli’s Principle
Assume you have an incompressible fluid moving in a steady, continuous stream, where viscosity forces are assumed to be
negligible (no friction losses). Several forms of energy are at play: (1) gravitational potential energy associated with the mass of
the fluid, Ep = mgz, (2) compressional potential energy of the fluid, PV, and (3) mechanical kinetic energy that is proportional
to the velocity of the fluid, Ek = mv2/2. The total energy is the sum of all forms. From the principle of conservation of energy, if
no work is done on the fluid, the total energy at two points along the path of the flow is the same:
v2
v2
m1 1 + m1 gz + P1V1 = m2 2 + m2 gz + P2V2 .
2
2
If z and density are the same along the flow (same fluid flowing in a horizontal pipe), we can cancel the gravitational potential
energy terms. Doing just that and dividing by the volume yields:
v2
v2
ρ1 1 + P1 = ρ2 2 + P2 .
2
2
Thus, changes in velocity along the flow (an acceleration) are associated with changes in pressure.
Bernoulli’s Principle holds significant implications for the calculations of aerodynamic lift, is used to measure velocity of
airplanes (the Pitot tube seen on the side of the cockpit of small jets), and makes it possible for wind-powered vehicles to travel
faster than the wind that propels them.
16
four feet, and asking students to predict which exerts a larger
pressure on the floor. Students are asked to cast their votes and
then calculate the pressures (assuming the mass of an elephant is
6000 kg, the mass of the ballerina is 45 kg, the radius of one foot
of the elephant is 30 cm, and the radius of the tip of the ballet
shoe is 1 cm). (Recall that the force [F] is equal to the weight [not
to be confused with mass] of the object: F = weight = mg, where
m is the mass and g is the gravitational acceleration 9.8 m/s2).
We use Activities 2.1 and 2.2 as powerful illustrations of the
concept of pressure. Hydrostatic pressure is demonstrated in
Activities 2.3 and 2.4. Although these two activities highlight the
same principle, students often comment that doing both activities greatly improved their understanding of hydrostatic pressure.
They were “forced” to transfer knowledge from one situation
to another and the processes prompted them to re-evaluate
their understanding. The use of multiple activities to illustrate
the same principle also provides the instructor with additional
opportunities for assessment. Activities 2.5 and 2.6 are designed
to demonstrate the concept of compressibility of gases under
pressure, where Activity 2.5 provides a qualitative illustration,
and Activity 2.6 is a quantitative presentation of Boyle’s Law. To
demonstrate Bernoulli’s Principle, we use Activity 2.7. Activities
are set up at stations, as described in Chapter 1, and can, alternatively, be used as class demonstrations.
Figure 2.1. Activity 2.1 setup and experiment with bed of nails (top) and a single
nail (bottom).
Explanation
When a balloon is placed on a bed of nails (Figure 2.1, top
left panel), the force that is applied is distributed over a large
area (the sum of the heads of all the nails in contact with the
balloon). The resultant pressure is not sufficient to cause the
balloon to pop (Figure 2.1, top right panel). When the balloon is
placed on a single nail, it takes only a weak force for the balloon
to pop because the force is now distributed over a smaller area
(the area in contact with one nail; Figure 2.1, bottom left panel),
and the higher pressure causes the balloon to pop (Figure 2.1,
bottom right panel). For that same reason, lying on a bed of
nails may feel prickly but will not hurt you, while stepping on
one nail may poke a hole in your foot. The same argument can
be used to explain why sharpening a chopping knife or an axe
makes them more effective for cutting.
Activity 2.1. Bed of Nails (Figure 2.1)
Materials
•
Two square wooden boards (same size); one board has a
single nail in the center; the other board has a grid of nails
(15 by 15 nails)
• Ring stand
• Balloons of the same material, size, and shape
• A ring to serve as a weight
We insert a small clear piece of tubing onto the ring stand pole
to make it easy to move the ring along the stand pole and be
placed on the balloon. However, any kind of weight that can be
placed on the balloon will work.
2.2. Perception of Weight (Figure 2.2)
Materials
•
Large, hollow steel ball (diameter 12.5 cm and a mass of 144 g;
from sciencekit.com)
• Small, solid steel ball (diameter 3.2 cm and a mass of 129 g;
from sciencekit.com)
• Two large identical funnels
• A balance for weighing each ball
Instructions to the Students
1. Predict what will happen to a balloon when you place it on
each of the boards and apply approximately the same force.
Explain your reasoning.
2. Test your prediction.
Instructions to the Students
1. Simultaneously, hold the two balls in the palms of your hands.
Which one feels heavier?
2. Choose a volunteer and ask this person to close his/her eyes.
Place each ball in a funnel and ask the volunteer to hold each
17
Instructions to the Students
Prior to the activity, we review the hydrostatic equations and
provide the students with the following instructions (some
may find that discussing the hydrostatic equation works best
AFTER doing part A).
Part A
1. You have a pipe with one small exit hole near the bottom and
several large holes plugged with rubber stoppers. You can fix
the height of the water column above the exit hole by simultaneously covering the bottom exit hole with your finger and
filling the tube until water flows out one of the upper large
holes (after removing a stopper from the hole). Make sure you
have placed the ruler perpendicular to the bottom of the pipe.
2. Before you use this apparatus: What do you expect will happen
when you fill the tube with water to the height of the first large
hole (from the bottom) and release your finger from the exit
hole? Explain your expectations in terms of the forces acting
on the fluid. What do you expect will happen when the water
height above the exit hole is increased? Why?
3. Test your predictions. Begin by removing the rubber stopper
from the lowest large hole. Simultaneously, hold your finger
over the small exit hole, and fill the pipe with water until it
runs out the hole the stopper was in. (Think: Why do we want
to maintain a fixed water level within the tube?) Using a ruler,
measure the height of the water column above the exit hole.
Then, remove your finger from the exit hole letting the water
run out, while you continually fill the pipe with water to maintain the same height of water column above the exit hole. Note
how far the water squirts when it first strikes the ruler. Replace
the stopper and repeat the steps for the next four holes,
working up one hole at a time.
4. Plot the distance at which the water hit the ruler as a function
of the height of the water column for each of the holes. Are the
data consistent with your prediction in Step 2?
5. Would the distance that the water travels, for any given hole,
change if the holes were bigger? Why?
Figure 2.2. Materials for Activity 2.2 (left) and experiment (right).
funnel by the bottom of the collar. Ask the volunteer to indicate which ball is heavier and record his/her answer. Repeat
this experiment with another volunteer(s).
3. Was the perception of weight when holding the funnels
different from the “free-hand” test? Why?
4. Weigh the balls to determine which one is heavier. Explain
your observations.
Explanation
When holding each ball in the palm of a hand, the large ball
feels lighter than the small ball. The force (F = mg) exerted by
the large ball is actually larger, compared to the small ball.
However, because the force is distributed over a larger area, the
pressure (P = F/A) is smaller, and it feels lighter. When the balls
are placed in the funnels and held by the collars, the surface
area to which the force is applied is similar for both balls and
you will notice that the larger ball is slightly heavier, which is
confirmed using a balance.
2.3. Ready, Set, Squirt (Figure 2.3)
Materials
•
A pipe with one small exit hole drilled near the bottom and
seven large holes drilled along it and plugged with rubber
stoppers (Figure 2.3, top). The separation between the hole
centers is 5 cm (can be varied). A simpler version of this
activity can be done using the mid sections of 2-liter soda
bottles taped together (Sharon Franks, UCSD, pers. comm.,
June 2009)
• A pipe with three different-size holes drilled at the same height
(Figure 2.3, middle)
• Large tub
Part B
1. Take the second pipe (with three holes of different diameters),
cover all three holes with your finger(s), and fill the pipe with
water. Place the ruler perpendicular to the bottom of the pipe.
Uncover one hole at a time and measure the distance at which
the water first strikes the ruler. Does your observation agree
with your reasoning in Step 5 above (Part A)?
•
Ruler
Jug with water
• Paper towels
•
18
Explanation
Part A
The weight of the water column exerts pressure on the water at
the level of the exit hole (imagine a cross-sectional area of the
tube at the level of the hole). This pressure is higher compared
to the pressure outside the hole (the atmospheric pressure),
causing water to squirt out once the finger has been removed.
As the height of the water column above the exit hole increases,
the pressure difference between the inside and the outside of the
exit hole increases, causing the water to squirt out to a greater
distance. Recall that hydrostatic pressure is proportional to the
height of the water column above the hole (the contribution of
air pressure is the same on both sides of the hole).
water level controlling holes
exit hole
Part B
Except for very small holes (where friction becomes important),
the size of the hole will not change significantly the distance to
which the water travels. One way to solve this problem mathematically (for the more advanced students) is to consider pressure (P = ρgz) as the potential energy (PE = mgz, where m is the
mass) per unit volume, V. Thus, PE/V = mgz/V = ρgz. As a parcel
of water squirts out of the column, most of its energy is transformed to kinetic energy (KE/V = ρv 2/2, where v is the velocity
perpendicular to the hole). From conservation of energy,
ρv 2/2 = ρgz, thus v = 2gz , that is, the velocity and hence the
distance a given fluid travels does not depend on the size of the
hole and is only a function of the height of the column (z).
The distance to which the fluid squirts can be predicted from
a simple argument familiar to students with a background in
mechanics. The fluid will arrive at the ground at t = 2H/g
seconds after leaving the hole, where H is the height of the hole
above ground, and at distance L = vt, where v = 2gz . In practice, the distance is decreased some, compared to the calculated
distance, due to friction with the sides of the hole and with the
air that the fluid travels through before arriving at the ground.
Figure 2.3. Materials for Activity 2.3, Part A (top) and Part B (middle). Students
performing Part A (bottom).
2.4. Manometer and Equilibrium Tubes
(Figure 2.4)
Materials
This activity can be further developed to illustrate the concept
of a reservoir (a large storage pool with inputs and outputs
whose level [volume] changes depending on the difference
between the inputs and outputs of water).
•
•
U-shaped manometer (made of supplies that can be found at
any hardware store: clear plastic tube cut into three pieces and
two elbows to connect the pieces of tube)
Water
Oil
• Equilibrium tube #1: arms of different shapes (sciencekit.com)
• Equilibrium tube #2: arms of different diameters
(sciencekit.com)
•
19
Instructions to the Students
Part C
1. Study the equilibrium tube with different arm diameters.
Predict what the water level will be in each arm (relative to each other) when you fill the apparatus with water.
Draw a qualitative diagram of your prediction and explain
your reasoning.
2. Test your prediction.
3. Does your observation agree with your prediction? If not, how
would you revise your explanation?
Prior to these activities, the students have reviewed Newton’s
Second Law, which, when applied to fluids, implies that in the
absence of other forces, fluid will flow from high to low pressure.
Part A
1. Predict what will happen when you fill the U-shaped manometer with water. How will the water level compare between
the two arms? Why? Sketch the manometer in cross section,
showing your prediction, and explain your reasoning.
(Hint: If the water is at rest [no flow along the tube], what can
you say about the difference in pressure between the bottoms
of each arm?) Fill the manometer until you can clearly see the
waterline in each arm, and compare what you observe with
your prediction.
2. What do you think will happen to the fluid level in each arm
if you add oil (enough to form a layer of approximately 5 cm)
to one arm? Why? If you predict a change, draw a qualitative
diagram of the new equilibrium.
3. Add oil. Does your observation agree with your prediction?
Explain.
Explanation
Part A
A manometer is a device that measures pressure based on the
fluid height. The simplest form of a manometer is a U-shaped
tube filled with a fluid. The level of the water in each arm of
the manometer is determined by the pressure that the air
column plus the water column exert on the bottom of the arm.
When one arm of the manometer is filled, water flows into the
other arm until the system reaches equilibrium and there is
no flow in the manometer, meaning that the pressure at the
bottom of both tubes is equal (P1 = P2 and P1 = gρwater z1 + Pair ;
P2 = gρwater z2 + Pair , thus z1 = z2 ). The height of the water column
in each arm will be the same. When oil is added atop the water
in one arm, the manometer reaches a new equilibrium: P1 = P2
with P1 = g(ρwater zwater1 + ρoil zoil) and P2 = gρwater zwater2 . Because
ρoil < ρwater , the fluid column in the arm with water and oil must
be higher than that in the arm with only water (air pressure
being equal in both).
This activity can be used as an analogy to the dynamic height
approach of calculating ocean surface slopes and for examining
the relationship between integrated density and the height of a
water column. The bottom of the U-shaped apparatus is analogous to the reference level of no water motion. At any height
above the oil-water transition, there is a pressure difference
between the two arms of the apparatus (hence, if we connected
the arms above the bottom, fluid would flow from the arm
containing oil + water to the arm containing water only until the
system reaches a new equilibrium).
Part B
1. Study the equilibrium tube with different-shaped arms.
Predict what the water level will be in each arm (relative to
the other arms) when you partially fill the apparatus with
water. Draw a qualitative diagram of your prediction and
explain your reasoning.
2. Test your prediction.
3. Does your observation agree with your prediction? If not, how
would you revise your explanation?
Part B
The shape or cross-sectional area of the arm(s) of a manometer has no effect on the water level. The height of the water
(or any other fluid) column in each arm is a function of the
pressure and the density of the fluid (z = P/ρg). Thus, after
the fluid is introduced to the column and the system reaches
equilibrium, the pressure at the bottom of each arm is equal
Figure 2.4. Materials used in Activity 2.4. The U-shaped manometer (Part A) is
seen in the background. In the foreground is an equilibrium tube with differentshaped arms (left) and equilibrium tube with different arm diameters (right).
20
(no flow) and the height of the water will be the same for each
arm, regardless of its shape. This observation explains why the
pressure at a given depth is the same pressure whether in a pool
or in a lake (assuming atmospheric pressure above the pool
and the lake is the same).
Part C
The same principle applies to the equilibrium tube with arms of
varying diameters. The height of the water column will be the
same for each arm. The only exception to this statement involves
the thinnest arm of equilibrium tube #2, for which another force
becomes important; surface tension at the rim of the glass acts to
pull the water to a higher level (this observation can be used as a
brainteaser, leading to another class focused on surface tension
and capillary action).
2.5. Shrinking balloons (Figure 2.5)
Materials
•
Vacuum container used for food preservation (found in
kitchen-appliance stores)
• Pressure apparatus (2-liter soda bottle fitted with a hand pump
that is used for keeping soda bottles carbonated and can be
found in many grocery stores)
• Two balloons of the same size (one filled with air, the other
with water)
• Marshmallows (Peeps are students’ favorites) and any other
items to be tested (e.g., tangerine, cherry tomato)
Instructions to the Students
1. Predict what would be the effect of reduced pressure on each
of the balloons.
2. Place the balloon filled with air in the vacuum container and
evacuate the air from the container by using the hand pump.
What happens to the balloon? Release the valve, allowing air to
get back into the container. What happens to the balloon now?
3. Repeat this experiment with the balloon that is filled with
water. Does the effect of pressure differ between the two
balloons? Why?
4. Based on your observations, what do you think will happen to
the marshmallow (and any other items to be tested) when you
evacuate the container?
5. Test your prediction.
6. Release the valve and observe the marshmallow. Explain
your observations.
Figure 2.5. (top) Materials for Activity 2.5. (middle) Testing an air-filled vacuum
container. (bottom) An air-filled balloon under atmospheric pressure (left) and
after air was pumped into the bottle (pressure increased; right).
7. Explore the second pressure apparatus. Compare/contrast
your observations on the behavior of the balloon filled with air
in this apparatus to the behavior of the balloon filled with air
in the vacuum container. What is the difference between this
apparatus and the vacuum chamber?
21
Instructions to the Students
A challenge:
1. How would you get a balloon full of air into the soda bottle?
2. How could you use this apparatus to demonstrate that air
has weight?
1. Record the volume of air in the syringe under conditions of
atmospheric pressure.
2. What do you think the volume of air in the syringe will be if
you place 2.5 lbs on top of the apparatus? What is the pressure
within the syringe?
3. What will happen to the volume of the air in the syringe if you
keep adding weights? By what percentage will it change by the
time you place 15 lbs on top of the syringe?
4. Test your predictions. Place a weight on the top of the syringe
(2.5 lbs) and record the volume of air. Place additional weights
(totaling 5 lbs, 10 lbs, and 15 lbs) and record the change in air
volume for each added mass. What do you observe?
5. Plot the added mass vs. the volume of air in the syringe. How
does the volume depend on the added mass? Does it agree
with your predictions? Do you feel a change in temperature as
you compress the air? Should you expect one?
Explanation
Objects that contain air cavities expand when the pressure
around them decreases, as occurs when evacuating air from the
vacuum container (Figure 2.5, top left panel). Because water is,
to a large extent, an incompressible fluid, the size of the balloon
containing water will be the same under low pressure and under
atmospheric pressure. A cherry tomato will behave similar to
the water balloon as it does not contain air pockets. A tangerine
or a marshmallow, on the other hand, contains air pockets,
and will expand when placed in a vacuum. When the valve is
released, air rushes back into the container, increasing the pressure (until it reaches atmospheric pressure), and the tangerine
and marshmallow will shrink, but not necessarily to their original sizes because the structure of the material has been altered
in the process (e.g., merging of air cavities in the marshmallow).
When we pressurize the soda bottle by pumping air into it, the
pressure around the balloon increases and it shrinks to a smaller
volume (increasing its internal pressure—compare the bottom
right and left panels of Figure 2.5). Releasing the pressure valve
brings the air-filled balloon back to its original size.
Challenge: To insert an air-filled balloon into the bottle,
place the opening of a balloon around the opening of the bottle,
leaving a small space to insert a straw between the balloon and
the wall of the bottle. As you blow into the balloon, air from
the bottle can escape outside through the straw, allowing the
balloon to expand. Tie a small knot and push the balloon inside
the bottle. This apparatus can be also used to demonstrate that
air has non-negligible mass by weighing the bottle at atmospheric pressure, then pumping air into the bottle and weighing
it again (the mass is retrieved by dividing by g, automatically
done by computer chips within balances).
2.6. Compressibility of Gases (Figure 2.6)
Materials
•
Compressibility of gases apparatus (Arbor Scientific, or a
homemade version can be easily assembled—a sealed 60-ml
syringe has a cross section of 1 in2)
•
Weights of known mass (we use 2.5-lb barbell weights)
Figure 2.6. (top) Materials for Activity 2.6. (bottom) The
apparatus once 15 lbs have been laid on its top.
22
6. By what percentage did the pressure increase in the syringe,
compared to the atmospheric pressure (the pressure applied by
a mass of 14.7 lbs on a square inch at Earth’s surface), when all
the weights were placed on the syringe (15 lbs; noting that the
cross section of the syringe is ~ 1 in2)? By what percentage did
the volume of the syringe change when the 15 lbs of weight
were added (assuming no change in temperature)?
7. Using your data, how do you expect the volume of the lungs
of a free diver to change when diving to 10 m? (Pressure
increases by one atmosphere every 10 m).
Note: It is difficult to find metric-system weights appropriate for
this set up. This activity can provide an opportunity to practice
unit conversion.
Explanation
In this activity, under normal atmospheric pressure, the volume
of air in the syringe is 46 ml. For an ideal gas at constant
temperature, T, the volume, V, of the gas varies inversely to the
pressure applied to the gas (Boyle’s Law: under constant temperature conditions the product of the pressure, P, and volume
of a gas, V, is constant → PV = constant and P = constant/V).
Thus, the addition of weights (increase in pressure) will reduce
the volume of air in the syringe. Adding 15 lbs of mass to
the syringe approximately doubles the pressure (compared
to normal atmospheric pressure), and the volume of air in
the syringe decreases by half, as expected from Boyle’s Law.
Similarly, when a free diver dives to a depth of 10 m, the pressure he/she experiences doubles relative to what it is at the
surface. As a result, the volume of his/hers lungs will be reduced
by half. Although we expect the gas in the syringe to heat up
as it is compressed, exchanges in temperature with the room
result in little or no perceptible change; hence, the assumption
of constant temperature is valid. This activity demonstrates
well the weight of the atmosphere, a weight we are mostly
unaware of in everyday life.
Figure 2.7. (top) A student attempting to fill the bag while holding the bag
against the lips. (bottom) When keeping the opening of the bag wide open and
blowing from distance toward the opening, the bag can be filled with only one
gust of air.
distance (Figure 2.7, bottom panel), which creates a low-pressure
area near the opening where velocity is high. This local low pressure brings in air from the surrounding atmosphere (where the
pressure is higher), and all the air flows rapidly into the bag. The
bag is not elastic and provides little resistance to the gushing air
(as long as it is not full).
References and Other
Recommended Reading
Denny, M.W. 1993. Chapters 3 and 4 in Air and Water, Princeton University Press,
Princeton, NJ.
Faber, T.E. 1995. Chapter 1 in Fluid Dynamics for Physicists, Cambridge
University Press.
Hewitt, P.G. 2008. Chapter 7 in Conceptual Physics Fundamentals. Addison Wesley.
Richardson, D., ed. 2005. The Encyclopedia of Recreational Diving, 3rd ed. PADI,
Santa Margarita, CA.
Vogel, S. 1996. Chapters 3 and 4 in Life in Moving Fluids. Princeton University Press,
Princeton, NJ, 484 pp.
Activity 2.7
To demonstrate Bernoulli’s Principle, we hand the students a
long plastic bag (Bernoulli bag; Arbor Scientific; Figure 2.7).
We ask one student to hold the open end of the bag and another
student to hold the closed end, so that it is held horizontal,
parallel to the floor. We then ask the students if they can fill the
bag with only one gust of air. The tendency of most students is
to seal the bag against their lips and blow air into it repeatedly,
requiring many breaths (Figure 2.7, top panel). A much more
effective technique is to blow into the opening of the bag from a
Other Resources
Sorbjan, Z. 1996. Hands-On Meteorology: Stories, Theories, and Simple Experiments.
American Meteorological Society, Washington, DC. A collection of hands-on
experiments designed around concepts of meteorology. Chapter 3 addresses
pressure. In addition to the experiments, the book contains historical narratives, references to important discoveries, and some stories about famous and
infamous scientists.
A YouTube movie containing a series of demonstrations of Bernoulli’s principle by
Julius Sumner Miller – Physics – Bernoulli:
Part 1: http://www.youtube.com/watch?v=KCcZyW-6-5o
Part 2: http://www.youtube.com/watch?v=wwuffpiYxQU&feature=related
23
Discrepant Events:
Awakening Students’ Curiosity
To attract students’ attention, provoke thought, and
initiate inquiry, educators sometimes use discrepant events
(Hassard, 2005; Chiapetta and Koballa, 2006). Such events
present surprises, causing students to wonder, “What’s
going on?” An example of a discrepant event is Activity 2.2.
Students feel that the smaller ball is “heavier,” but after
measuring the mass of each ball they are surprised to
discover that the larger ball is the heavier of the two. That
finding causes them to rethink the concepts of pressure
and weight and helps them to differentiate between force
and pressure (force per unit area). Compendia of discrepant
events related to various science concepts are readily available on the Internet and in science teaching texts. For
example, Liem (1987) has compiled over 400 discrepant
events that use simple materials—with sketches, questions,
and explanations—for the science teaching of elementary
through college students.
An effective discrepant event often requires very little
instruction. For example, at the start of class, an instructor
may silently fill an empty, transparent 2-liter soda bottle
one-quarter of the way with very hot water, swirl the water
around for a few seconds to warm the whole bottle, pour the
water out of the bottle, screw the cap on tightly, and then set
the bottle in full view of the students. While the instructor
takes roll, the bottle crumples inward in several places.
Invariably, the students become intrigued and start asking
questions about the bottle and the water. The instructor can
guide the dynamics of the students’ questioning and hypothesizing as to the explanation of the bottle’s collapse, leading
to a discussion of the Ideal Gas Law and the relationship
between temperature, pressure, and volume.
Presenting students with a puzzle in the form of an
unexpected event challenges their preconceptions, whether
based on knowledge or intuition, triggers curiosity, and
increases motivation to find a solution. Through the
process of inquiry, leading to discovery, students can reach
new levels of cognitive understanding and develop better
problem-solving skills (Piaget, 1971). Discrepant events
need not be physical activities; they may be presented
through films, descriptions of events, or field observations
(e.g., reversed magnetism in rocks) that present intriguing
paradoxes. Discrepant events can be used to achieve specific
pedagogical goals—initiating a lesson and getting students’
attention, eliciting questions from students, identifying and
addressing students’ misconceptions, causing students to
continue thinking about a process or a problem after the end
of a lesson, testing whether students can apply what they
have learned to explain a similar, but unexpected phenomenon, and serving as a part of a formal lesson evaluation.
Whenever a discrepant event is presented, it is important to
allow students sufficient time to think about, discuss, and try
to explain the event.
References
Chiappetta, E.L., and T.R. Koballa Jr. 2006. Science Instruction in the Middle
and Secondary Schools: Developing Fundamental Knowledge and Skills
for Teaching, 3rd ed. Pearson/Merrill Prentice Hall, Upper Saddle River,
NJ, 320 pp.
Hassard, J. 2005. The Art of Teaching Science. Oxford University Press, 496 pp.
Liem, T.L. 1987. Invitations to Science Inquiry, 2nd ed. Science Inquiry
Enterprise, Chino Hills, CA, 488 pp.
Piaget, J. 1971. Biology and Knowledge. University of Chicago Press,
Chicago, IL.
24
Chapter 3. Buoyancy
PURPOSE OF Activities
weight of the displaced fluid (Archimedes’ Principle). If the
weight of an object (in air) is greater than the weight of the
displaced fluid, it will sink; if it is less, it will float.
In mathematical terms, the two opposing forces can be written
(based on Newton’s Second Law) as
This set of activities was designed to help students better understand the underlying principles of buoyancy. Most students
have heard the term buoyancy and have experienced it when
entering the ocean, a pool, or a bath. Some may even be able
to recite Archimedes’ Principle. However, our experience has
shown that students often struggle when asked to address questions related to buoyancy. Research conducted at the University
of Washington found that many science and engineering
majors lacked an understanding of buoyancy even after taking
introductory physics classes that taught hydrostatics (by a standard instructional approach) and were not able to predict or
explain the floating and sinking behaviors of different objects
(Loverude et al., 2003).
We introduce buoyancy to our students after they have
already completed the labs on density (Chapter 1) and pressure
(Chapter 2). In the density lesson, students examined sinking and
floating behaviors of various objects as a function of their densities, but did not investigate the underlying principles governing
these behaviors. The activities below allow students to apply
knowledge gained in the previous two lessons to further explore
the factors governing sinking and floating.
Fbouyancy = mfluid g = ρfluidVdisplaced g
and
Fgravity = mobject g = ρobjectVobject g.
Where mfluid and mobject are the masses of the displaced fluid and
the object, g is the gravitational acceleration constant, ρfluid and
ρobject are the densities of the fluid and the object, and Vdisplaced
and Vobject are the volumes of the displaced water and the object.
When the object is fully immersed, Vdisplaced = Vobject. From the
definition of density, recall m = ρV.
The difference between the two forces determines whether the
body sinks, floats, or remains neutrally buoyant.
∆F = Fgravity – Fbouyancy = Vobject g (ρobject – ρfluid )
When ∆F > 0, the object sinks. When ∆F < 0, the object floats.
And when ∆F = 0, the object remains at its depth (it is neutrally
buoyant; that is, ρobject = ρfluid). So, the key to keeping a ship
afloat, whether it is made of wood, steel, or concrete, is to have it
displace a volume of water that weighs more than the ship itself.
BACKGROUND
When an object is immersed in a fluid, the fluid is displaced to
“make room” for the object. For example, when you get into a
bathtub, the water level rises. The amount of water an object
displaces when fully submerged is equal to its own volume
(e.g., recall the measurements of rock volume in Activity 1.3).
The immersed object is subjected to two forces: (1) a downward force—the gravity force, which increases as the mass of
the object increases, and (2) an upward force—the buoyancy
force, which increases as the density of the fluid increases.
When the downward gravitational force on an object is greater
than the upward buoyancy force, the object sinks; otherwise,
the object floats.
The buoyant force arises from an imbalance in the pressures
exerted on the object by the fluid. Because pressure increases
with depth, the bottom of the immersed object experiences a
higher pressure than does its top; therefore, the object experiences an upward force. The resulting upward force equals the
Applications to the Ocean
Buoyancy is one of four dominant forces in ocean dynamics (the
other three are gravity, wind stress, and friction), and understanding buoyancy is key for understanding density-driven
circulation. The ocean’s large-scale thermohaline circulation,
for example, is attributed to latitudinal differences in buoyancy
forcing, due to high-latitude versus low-latitude differences in
water temperature. Cooling and evaporation make seawater
denser, so surface waters subjected to these conditions become
less buoyant, tending to sink. Warming and precipitation, in
contrast, decrease seawater density, so surface waters subjected
to these conditions become more buoyant, tending to float
at the ocean’s surface.
The level at which an object floats in a liquid (e.g., seawater
or magma) depends on the balance between the gravitational
and buoyancy forces to which the object is subjected. Earth’s
25
understanding. The two other activities (3.3 and 3.4) are what
we term “open inquiry”: students are not provided with much
instruction and are expected to synthesize and apply knowledge learned in the previous lessons on density and pressure
(Chapters 1 and 2 in this document) to explain a given phenomenon and construct a float. Applications to the aquatic environment are discussed during the review and discussion session at
the lesson’s end. The activities are set up at stations as described
in Chapter 1.
lithospheric plates, for example, float on the asthenosphere (the
upper mantle) at an equilibrium level (a buoyancy equilibrium
called “isostasy”). When a buoyant equilibrium is disrupted,
the object will sink or rise until a new buoyancy equilibrium is
reached. This process is termed “isostatic leveling.” The effects of
isostatic leveling can be seen near mid-ocean ridges where freshly
formed lithosphere is cooling and adding weight to the underlying ridge (the gravity force has increased) and on continental
plates where large glaciers have recently melted (the gravity force
has decreased). Changes in the buoyancy equilibrium of lithospheric plates will cause a relative rise or fall in sea level along the
coast associated with the plate.
Many marine organisms face the challenge of buoyancy
regulation. Proteins, connective tissues, skeletons, and shells all
have densities greater than the density of seawater. Organisms
with high body density may sink below their optimal growth
zone (e.g., phytoplankton sinking below the photic zone) and
be exposed to changes in pressure, light, and temperature. In
response to these challenges, marine organisms have developed a
variety of strategies to control their buoyancy. Examples include
the selective exchange of heavier ions for lighter ions, storage of
fat and lipids, and the use of gas-filled cavities.
Buoyancy is also a fundamental principle in the design of
boats, ships, submarines, and autonomous underwater vehicles
(AUVs), with the latter being the state-of-the-art in ocean technology and exploration. Autonomous gliders and floats, which
carry a variety of sensors (e.g., temperature, salinity, and optical),
move up and down in the water column by changing their
volume and thus the buoyancy force acting on them. The principle of operation is the exchanges of fluid between an internal
incompressible tank and an external inflatable bladder. For an
illustration of a float that uses this mode of buoyancy regulation,
visit: http://www.argo.ucsd.edu/FrHow_Argo_floats.html.
Activity 3.1. Mayday! (Figure 3.1)
Materials
• Archimedes’ box (a box with horizontal gradation marks
every 1 cm)
• Spring scale
• 5-g and 10-g weights
• Container with water
• Ring stand
• Ruler
• Balance
Note: The special box, spring scale, and weights were all
obtained from sciencekit.com.
Instructions to the Students
1. Assume that the box is a cargo ship. As a crew member, you
need to determine the maximum cargo weight (in grams)
that you can load on your ship without sinking it. At the
point of maximum loading, the box (your ship) will be
fully—but just barely—submerged, so that its top just touches
the water’s surface. Based on what you know about buoyancy and Archimedes’ Principle, how would you determine
the maximum amount of cargo? Explain your rationale.
(Hint: Think about the weight of an object in air and in water
[fully immersed] and the volume it displaces. Use the spring
scale and ruler to obtain any measurements that can help with
your prediction. To use the spring scale, attach it to the ring
stand and use the hook to hold the box).
2. Add the predicted maximum amount of cargo to your box
(ship), close the lid, and test your prediction by placing the
loaded ship in the tub of water and observing whether it is
fully immersed but not sinking.
3. If your prediction was correct, what is the mass of the ship +
cargo in air? What is the mass of the ship + cargo in water?
What are the volume and mass of the water that was displaced?
Description of ACTIVITIES
We begin the lesson with a short introduction or review of the
forces that act on an immersed object, after which students
engage in the activities below, working in small groups. Two of
the activities (3.1 and 3.2) are quantitative representations of
Archimedes’ Principle, allowing students to explore the relationships among the mass of an object, the mass of the volume
it displaces (proportional to the buoyancy force), and its sinking
or floating behavior. We ask students to conduct both activities
(the order does not matter). By doing this, we can reinforce the
principles of buoyancy, allow students to practice transfer of
knowledge learned in one situation to another, and test their
26
4. If your prediction was not correct (i.e., if your boat sank or
floated above the water’s surface), revise your prediction and
test it again.
5. Once you find the maximum allowable cargo weight, add an
additional 25 g to your cargo and place the box in the water.
What happens to your ship now? Why?
6. What is the new weight of the ship + cargo in air? Predict the
weight of the ship + cargo in water. Use the spring scale to
measure the weight of the ship + cargo in water. Does your
measurement agree with your prediction?
7. What is the weight of the water that is displaced? How does it
compare to the weight of the ship + cargo in air and the weight
of the ship + cargo in water?
8. Can you now explain why an object submerged in water
“feels” lighter?
Note to instructors: If your students struggle to predict the
amount of maximum cargo based on Archimedes’ Principle,
then suggest that they approach the problem using the following
few steps:
1. Measure and compute the mass and volume of the box without
the weights. Add weights in increments of 25 g. With each
addition, measure:
a. The weight of the box outside the water (using the
spring scale)
b. The weight of the box in the water
c. The height of the section of the box that is immersed in
water (each mark on the box is 1cm)
For each increment, calculate the volume of water displaced
by the box.
2. Plot the height of the box section immersed in water as a function of the weight of the box + added weights. Do you see any
pattern between the mass of the box + weights (in air) and
the volume displaced? What is the weight of the box in water
in each case?
Once the students complete these steps, have them do
Steps 3–4 above.
Figure 3.1. Apparatus for Activity 3.1 in air (left, with two weights lying on the
table) and in water (right).
this case, Fbuoyancy is proportional to the displaced volume. The
maximum mass that can be added to the box without sinking it
is 75 g (mbox + mweights= 25 g + 75 g = 100 g). When the box barely
floats, Fgravity is equal to Fbuoyancy (recall Fgravity = mg).
When students conduct this activity in small steps, by adding
mass in increments of 25 g, they can closely examine the relationship between the mass of an object in air, the displacement of
water (immersion depth), and the apparent mass of the object in
water, as shown in the table below.
Added
mass
(g)
Total weight
in air (box +
weights) (g)
Weight in
water (g)
Immersion
depth (cm)
Displaced
volume
(cm3)
0
25
0
1
25
25
50
0
2
50
50
75
0
3
75
75
100
0
4
100
By Archimedes’ Principle, the box sinks when its weight
exceeds that of the displaced water. Thus, when an additional
25 g is added to bring the total mass of the box + weights in air
to 125 g, which is larger than the mass of the volume displaced
(100 g), the “ship” sinks. The weight of the box + weights in water
is 25 g, which is proportional to the difference between the gravitational and buoyant forces.
Because g is constant, we consider only the masses of the box
and the displaced water, but we emphasize to the students that
mass and weight should not be confused (weight = mg). It is
also important to explicitly discuss with students the difference
between the case of a floating object and the case of a submerged
Explanation
The box we use for this activity has a 5 cm x 5 cm = 25 cm2 base
and a height of 4 cm. Thus, its volume is 100 cm3 (including
its lid). The empty box weighs 25 g; hence, its density is
0.25 g/cm3. When the box is fully submerged, it displaces its
volume (100 cm3); therefore, the weight of the displaced water is
100 g (1 cm3 ≈ 1 g). According to Archimedes’ Principle, when
the box is neither sinking nor rising, Fbuoyancy = Fgravity, where
Fbuoyancy = ρwaterVdisplaced g. Because ρwater and g are constant in
object. In both cases, the magnitude of the buoyant force equals
27
the mass of the water displaced. However, for a floating object,
the volume that is displaced (the buoyant force) is determined by
the weight of the object divided by the density of the fluid; for a
fully submerged object, the volume displaced is determined by
the volume of the object (density does not play a role).
Based on the volume of the unknown ballast liquid that
you needed to draw in, how do you think the density of the
unknown liquid compares to that of freshwater?
Explanation
The ball we use for this activity has a density of 0.7 g/cm3, which
is less than the density of water (1 g/cm3); hence, the ball floats.
Because the ball’s volume remains constant, the only way to
make this “submarine” neutrally buoyant (fully submerged) is
to add mass by pulling out air (with the syringe) and replacing
it with water. The mass of the ball is 124.5 g and its volume
is 176 cm3. When the ball is fully submerged, it displaces
176 ml (cm3) of water that weighs 176 g. Therefore, approximately 52 g (about 52 ml) of tap water must be added to make
the ball’s density equal to that of water (i.e., to make the ball
neutrally buoyant). When students put the ball in the “unknown
liquid,” they find that a larger volume of water is required to
achieve neutral buoyancy, indicating that the unknown solution (e.g., sugar water) is denser than freshwater, increasing the
buoyant force acting on the sub.
Activity 3.2. Archimedes Ball (Figure 3.2)
Materials
•
•
•
•
•
•
•
Archimedes ball (from sciencekit.com)
60-ml syringe
Piece of tubing
Scale
Caliper
Container with water
Container with a sugar solution, labeled “unknown liquid”
Instructions to the Students
1. Imagine that the plastic ball is a submarine. You want it to
remain under water such that the stopper only is just above
the water surface (i.e., the submarine is neutrally buoyant).
Calculate how much ballast water do you need to add to the
submarine so that it is neutrally buoyant? (Hint: If you are not
sure where to begin, draw the submarine and the forces acting
on it when it is immersed in water).
2. Check your prediction (calculation) by placing the ball in
a container of water and drawing in freshwater, using the
syringe. The markings on the syringe will indicate how much
water is being added to the ball. Does the volume that you
obtained experimentally agree with your calculations?
3. Place your “submarine” in the “unknown liquid” and draw in
the unknown liquid until the submarine is neutrally buoyant.
Activity 3.3. Designing Floats (Figure 3.3)
Materials
•
•
•
•
•
Containers with freshwater and salt solution
Two beakers or deep tubs
Film canisters or small vials
Weights (washers, pennies, etc.)
Additional miscellaneous supplies: balloons, rubber bands,
tape, drinking straws, plastic aquarium tubing, glue guns
and glue, paper clips, duct tape, bubble wrap, pipe cleaners,
syringes, corks, packing peanuts (you don’t need everything;
these are only examples)
• Scale
• Caliper or ruler
• Graduated cylinder
• Aquarium with stratified fluid (saltwater and freshwater)
Note: The salt solution in the aquarium should be the same as in
the container of saltwater mentioned at the top of the list.
Instructions to the Students
You are funded to design two autonomous floats that will carry
sensors (washers) to measure various hydrographic properties (e.g., temperature, salinity) and biogeochemical properties
(e.g., oxygen, chlorophyll fluorescence, turbidity) in the Gulf
of Maine. One float should be able to drift at the surface. It
should float such that the top of the cap is just above the water
Figure 3.2. Apparatus for Activity 3.2.
28
Activity 3.4. Cartesian Diver (Figure 3.4)
This classic science experiment is named after René Descartes,
a French philosopher, mathematician, and scientist. It demonstrates buoyancy (Archimedes’ Principle) and the relationship
between pressure and volume in gases (Ideal Gas Law).
Materials
• A sealed soda bottle filled with tap water (colored water
works best)
• A plastic pipette weighted with metal nuts and/or washers
Note: For instructions on how to build a Cartesian diver, see, for
example, http://www.raft.net/ideas/Pipette%20Diver.pdf.
Instructions to the Students
1. Squeeze the bottle. Why is the half-closed pipette inside the
bottle sinking? Why does the pipette rise when you release
the bottle?
2. Explain the behavior of the pipette in terms of pressure and
Archimedes’ Principle.
Figure 3.3. A student testing Activity 3.3 “floats” in a stratified tank.
Explanation
surface. The other should float at the pycnocline (the location
where the density changes the most) without touching the
bottom of the tank.
Your first goal is to design a prototype of the floats, as a
proof of concept, to be presented to your program managers
(classmates). You have at your disposal a bucket with surface
water (freshwater) and one with deep water (salt solution). In
your presentation, describe the design of your floats and your
approach for determining their sinking and floating behaviors. At
the end of the class, you will be asked to demonstrate that indeed
one of your prototypes remains at the surface while the other
hovers at the pycnocline in a stratified tank.
According to Pascal’s Law, pressure applied to a fluid is transmitted throughout the fluid. When you squeeze the bottle, you
increase the pressure within the bottle and the open pipette
within it. The pipette in the bottle contains air. As a result of the
increase in pressure, the volume of the air trapped inside the
pipette decreases and water rises within the pipette, replacing
Explanation
We use this activity to add a healthy competitive component to
the lesson. From our experience, most students first approach
this problem by trial and error. We therefore encourage them,
using probing questions, to approach it using Archimedes’
Principle. At the end of the lesson, as part of the group discussion, each team tests the floats in a large aquarium with a stratified water column. (Be sure to use the same saltwater solution
that the students used in their containers.)
Figure 3.4. A Cartesian diver.
29
some of the air space. (Recall the Ideal Gas Law: PV = nRT,
where P is pressure, V is volume, n is the number of moles of gas,
and R is the universal gas constant. For constant temperature,
increasing pressure results in decreasing volume.) Because the
density of water is greater than that of air, the density of the
pipette system (pipette + air bubble + water) increases enough
that the pipette sinks.
Supplementary Activity (Figure 3.5)
For assessment, we administer a quiz (see p. 31) on concepts
covered in this lesson and the previous ones on density and
pressure as well as a problem-solving challenge. For the challenge, we present students with a well-known question: “You
have a large rock on a boat floating in a pond. When you throw
the rock overboard and it sinks, will the level of the pond rise,
drop, or remain the same?”
To solve this problem, one ought to compare the volume of
water displaced due to the rock is in the boat (Vdisplaced_b ) to the
volume displaced when the rock is fully submerged (Vdisplaced_s ).
Which is greater? Considering first the case of the rock in the
boat, by Archimedes’ Principle, that the weight of the rock
(neither rising nor sinking) equals the weight of the displaced
water: mobject g = mdisplaced_b g. Also, from the definition of density,
mobject = ρobjectVobject , mdisplaced = ρfluidVdisplaced . Combining these two
bits of information yields the volume displaced when the rock is
in the boat: Vdisplaced_b = Vobject ρobject /ρfluid . Considering now the case
of the submerged rock, this volume of displaced water is equal to
the rock’s own volume: Vdisplaced_s = Vobject . Finally, to predict what
happens to the water level when we toss the rock overboard, the
two displacement volumes are compared by looking at their ratio:
Vdisplaced_b /Vdisplaced_s = ρobject /ρfluid . Because the rock sinks in water, we
know that ρobject > ρfluid , which tells us that Vdisplaced_b > Vdisplaced_s : the
volume of water displaced by the rock in the boat is larger than
the volume displaced by the submerged rock. Thus, when you
throw the rock overboard, the pond’s water level will drop. Note:
the volume of water displaced due to the boat’s own weight is the
same whether the rock is in it or not and hence plays no role.
We first give students a few minutes to think individually
about the problem, then ask them to vote on whether they think
the water level will rise, drop, or remain the same. We always get
votes for each option. We then group the students according to
their “vote.” Each group must come up with an argument (physical explanation) that supports their prediction (or discover in
the process that their prediction needs to be revised) and present
it to the entire class.
Figure 3.5. The water level when the weight is placed in the boat (labeled as
“anchor in boat”) and when the weight is submerged under water (labeled as
“anchor in water”).
After each group has presented, we test their predictions (you
will need a child’s toy boat, a weight or a large rock, and a tub
filled with water). We place a child’s toy boat in a clear tub filled
with water and load it with a weight or a large rock. We ask a
student to mark the water level in the tub, to drop the weight
(rock) into the water, and then to mark the new water level
(Figure 3.5).
With this kind of assessment, students do not feel the pressure
of being “tested,” yet they are forced to apply their knowledge,
identify gaps in their understanding, and seek better explanations
to fill these gaps. Instructor(s) move among groups as they form
their explanations, assess the level of each student’s involvement, and identify areas of difficulty. Any concepts identified as
problematic are later reviewed during the demonstration. As an
alternative assessment, we use the five-block problem described
in Loverude et al. (2003).
References and Other
Recommended Reading
Denny, M.W. 1995. Chapters 3 and 4 in Air and Water. Princeton University Press,
Princeton, NJ.
Hewitt, P.G. 2008. Chapter 7 in Conceptual Physics Fundamentals. Pearson
Addison-Wesley.
Loverude, M.E, C.H. Kautz, and P.R.I. Heron. 2003. Helping students develop an
understanding of Archimedes’ Principle. I. Research on student understanding.
American Journal of Physics 71(1):178–1,187.
Vogel, S. 1996. Chapters 3 and 4 in Life in Moving Fluids. Princeton University Press,
Princeton, NJ.
Other Resources
Sorbjan, Z. 1996. Hands-On Meteorology: Stories, Theories, and Simple Experiments.
American Meteorological Society. Washington, DC. A collection of hands-on
experiments designed around concepts of meteorology. Chapter 7 addresses
buoyancy. In addition to experiments, the book contains historical narratives, references to important discoveries, and stories about famous and
infamous scientists.
30
Assessing Student Learning
Assessing students’ learning is an essential and sometimes
challenging aspect of teaching. Pen-and-paper tests are a
common form of assessment, though they tend to test more
for memorization than for deeper understanding, synthesis,
and application of knowledge. Pressured by administrations, society, and students themselves to provide grades,
educators often fall back on simple forms of objective tests
(e.g., multiple choice). However, test results may not reveal
why students succeeded or failed. If the goal is to determine
how well—not just how much—students are learning,
then a case can be made for employing assessment procedures that reflect the full range of our educational goals
(e.g., Fink, 2003). This is not to say that pen-and-paper tests
don’t have a place in formal education; we use essay exams
and multiple-choice tests in our own classes. However, we
maintain that a broader range of assessment methods should
be considered and used to assess not only student learning
but also our effectiveness as educators. These methods
include both formal evaluation (e.g., research papers, laboratory activities, oral presentations, oral exams) and informal
evaluation (e.g., observing students’ behavior during class
and their participation in discussions) (Hassard, 2005;
Feller and Lotter, 2009). Our goal in this short essay is not
to provide a comprehensive review of assessment tools or
point out the best assessment practice. Rather, it is to share
our experience and stimulate the reader to think about the
value of assessment and how it can be used more effectively
in the classroom to enhance learning. Practices should
vary depending on learning goals, the number of students
in class, their backgrounds, and the classroom setup. The
reliability of assessment and evaluation may be increased
by using several different methods to measure the same
expected learning outcomes.
With very large classes, hands-on, inquiry-based activities and assessment methods other than multiple-choice
or short-answer tests are more difficult to implement, but
there are ways in which traditional assessments, such as
multiple-choice tests, can become part of an active learning
process. Following Fink (2003), we give students a weekly
multiple-choice quiz and ask them to complete it initially as
individuals. After collecting the individual quizzes, students
are asked to retake the quiz, this time as a team of three to
four students. The team has to reach consensus for each
answer. For direct feedback, we give each team a prefabricated
scratch-off answer sheet (similar to a lottery ticket; see http://
www.epsteineducation.com/multichoice.php). Students
scratch off the covering to reveal if the answer they chose is
correct (showing a star) or incorrect (showing a blank square).
In this process, students re-assess their understanding and
are encouraged to communicate their ideas in a less stressful,
more collaborative environment. We tend to keep the same
teams throughout the semester. To foster healthy competition,
we record the number of points each team earns per week
(based on the number of correct answers), and the winning
team is awarded a pizza party at the end of the semester.
Another tool we use is a reflective journal in which
students assess their own learning. We first tried the traditional approach, using a lab notebook as a journal, but
students did not respond well; the journals became a collection of information and facts rather than a reflection on
learning. Students responded very well, however, when we
switched to Web-based blogs. Each student creates a blog
(e.g., on www.blogger.com), a medium that proved to be
more comfortable and familiar. Each week, students respond
to guiding questions that prompt them to comment on new
concepts they have learned, identify weaknesses in their
understanding, raise questions, and identify aspects of the
lesson that were and were not useful. Only instructors have
access to the blogs, or they provide weekly feedback to each
student. Reflective blogs provide instructors with immediate
feedback that can be used to align instructional strategies
and expected learning outcomes with student understanding. Blogging encourages students to think critically
about the material after each lesson and provides a means
to assess their understanding on a regular basis rather than
only at the course’s end.
Recommended reading
Hassard, J. 2005. The Art of Teaching Science. Oxford University Press, 476 pp.
Feller, R.J., and C.R. Lotter. 2009. Teaching strategies that hook classroom
learners. Oceanography 22(1):234–237. Available online at: http://
www.tos.org/oceanography/issues/issue_archive/22_1.html (accessed
August 12, 2009).
Fink, L.D. 2003. Creating Significant Learning Experiences: An Integrated
Approach to Designing College Courses. Jossey-Bass, San Francisco,
CA, 320 pp.
31
Chapter 4. HEAT AND TEMPERATURE
PURPOSE OF ACTIVITIES
on different materials. Commonly used thermometers measure
temperature by means of a change in the volume of a liquid
(e.g., bulb thermometers filled with mercury or alcohol) or a
change in the electrical resistance of a substance (e.g., ceramicor polymer-based thermistors).
Heat is defined as internal (kinetic and potential) energy that
is being transferred from one substance to another (e.g., Hewitt,
2008). The direction of heat transfer for substances in thermal
contact is always from the higher-temperature substance to the
lower-temperature substance. This rule does not mean, however,
that heat is being transferred from a substance with more internal
energy to a substance with less internal energy. Recall that
temperature is not directly proportional to the internal energy
of a substance; temperature is only a measure of the kinetic (and
not the potential) part of the internal energy. Conservation of
energy implies that when heat is transferred between systems, the
energy lost in one system is gained by the other. Heat has units of
energy. In the SI (metric) system, the units are joules. Other units
commonly used for heat are BTU (British Thermal Units) and
calorie (1 calorie = 4.18 joules). (Note: The food-related Calorie
[with a capital C] equals 1000 calories, or one kilocalorie.)
Different substances have different thermal capacities for
storing heat. The heat capacity of a substance is defined as the
amount of heat needed to raise its temperature by 1°C. The
specific heat capacity (Qs) is the heat capacity per unit mass.
Water has one of the highest values of specific heat capacity
of any liquid: Qs = 4186 J/(kg°C) (= 1000 calories/kg°C). The
specific heat capacity of air is about one-fourth that of water:
Qsair = 1006 J/(kg°C). This difference between the heat capacity
of water and air is even more striking considering that specific
heat is measured on the basis of mass, and the density of water is
about 1000 times greater than the density of air. Thus, for a given
volume, it takes approximately 4000 times more energy (heat) to
raise the temperature of water 1°C as compared to air. Similarly,
when water cools, it releases 4000 times more heat than is
released when the same volume of air cools (for a video demonstration of the difference between the heat capacities of water
and air see http://www.jpl.nasa.gov/video/index.cfm?id=827).
The specific heat of water is also much higher than the specific
heat of rocks and soil.
The higher heat capacity of water allows the ocean to absorb
A good grasp of the underlying principles of thermal physics is
essential for understanding how the ocean functions and how it
impacts climate. Thermal physics is one of the science subjects
that students are familiar with and experience on a daily basis,
but intertwined with the experiential knowledge they bring
to class comes a mixed bag of misconceptions that must be
identified and addressed (Carlton, 2000). Example misconceptions include an inability to differentiate between heat and
temperature, the notion that transfer of heat will always result
in a temperature rise, and a misunderstanding of the concept of
latent heat (Thomaz et al., 1995). Another popular misconception concerns confusion regarding the timing of maximum
heat flux and maximum temperature—for example, the time
of day when Earth’s heat flux is largest vs. the time of day
when the mean air temperature is highest, or the time of year
of maximum heat flux vs. maximum mean water temperature
in an ocean or a lake. The purpose of this set of activities is to
review basic concepts of thermal physics and to highlight applications to ocean processes. Thermal physics is a vast field, and
we do not attempt to cover all aspects of it. Here, we focus on
the concepts of heat transfer (conduction, radiation, and convection), latent heat, and thermal expansion. These laboratory
activities are completed over two class periods.
BACKGROUND
Temperature is a quantity that indicates how warm or cold
an object is relative to some standard. It is proportional to the
average kinetic energy associated with the motion of atoms and
molecules in a substance. The Celsius scale (°C) is commonly
used to measure temperature. This scale is calibrated to the
physical properties of pure water, where the freezing (or triple)
point at sea level pressure was arbitrarily set at 0°C and the
boiling point was set at 100°C. The familiar Fahrenheit (°F)
scale is calibrated so that the boiling point of water is 212°F and
its freezing point is 32°F. To convert degrees Celsius to degrees
Fahrenheit: multiply by 1.8 and add 32 (°F = 1.8 x °C + 32).
The Kelvin scale (denoted as K) is known as the absolute
temperature scale, and its zero point is equivalent to -273.16°C
(i.e., K = °C + 273.16). Temperature is not measured directly;
instead, it is measured indirectly through temperature effects
32
or release large amounts of heat with relatively small changes in
temperature compared to the atmosphere or land, both of which
have much lower heat capacities. The ocean, therefore, serves as
an important heat buffer by keeping Earth’s temperature from
rising or falling rapidly. This buffering is why coastal locations
experience smaller changes in temperature between day and
night and between seasons than do nearby inland locations. Land
warms up and cools down faster than the ocean under the same
conditions of solar radiation.
Latitudinal variations in solar energy flux result in large latitudinal variations in temperature. The ocean plays a key role in
moderating Earth’s climate, not only by storing/releasing large
quantities of heat (due to the high heat capacity of water) but also
by transporting heat from higher-temperature equatorial regions
to lower-temperature polar regions (e.g., via currents such as
the Gulf Stream; Gill, 1982). Without heat transport by ocean
currents and winds, differences in temperatures across latitudes
would be significantly higher. Mechanisms of heat transport are
discussed in more detail below, along with the activities that we
use to demonstrate them.
rate of energy absorption equals the rate of energy radiation.
The quantity and quality (wavelength) of radiated energy
depends solely on the temperature of the object. A conceptual
model used to describe the relationship between an object’s body
temperature and its emitted radiant energy is that of a “blackbody.” A blackbody refers to an object that completely (100%)
absorbs all electromagnetic radiation that arrives at its surface.
No electromagnetic radiation is reflected or passes through;
therefore, the object appears black. The energy, E, radiated by a
blackbody per unit of area per unit of time is proportional to the
fourth power of its temperature, T (in Kelvin): E = σT 4 where
σ = 5.7 x 10-8 W/m2 K4 (Stefan-Boltzmann’s Law). This relation
implies that if the temperature of a body doubles, the amount of
heat it radiates will increase sixteenfold.
Radiation does not occur at one wavelength, but across a spectrum of wavelengths. The peak of the spectrum (i.e., the frequency
or wavelength for which the radiation intensity is highest) is
inversely related to the temperature (Wien’s Law). Thus, as the
temperature of a body increases, the peak wavelength of radiation
shifts toward shorter wavelengths. For example, the transfer of
energy from the sun to Earth’s surface is accomplished primarily
by radiation. The surface temperature of the sun is 6000 K, and
its radiation peak is in the visible wavelength range (relatively
short wavelengths). Earth’s surface and atmosphere also emit
radiation, but their temperatures are lower than that of the sun
(~ 300 K), and the radiation peak is in significantly longer wavelengths (infrared). This concept is central for understanding the
greenhouse effect. The atmosphere is transparent to the incoming
or reflected shortwave solar radiation but not to the longwave
(infrared) radiation emitted from Earth’s surface or the atmosphere. Thus, energy from the sun reaches Earth’s surface, where
it is absorbed by land and ocean. The radiated longwave energy,
however, is absorbed by atmospheric gases and thus gets trapped
in the atmosphere, which acts as a “blanket.”1
Conduction refers to the transfer of heat between two bodies
of different temperatures in physical contact with each other.
Heat is transferred by vibration and collision of molecules.
Mechanisms of Heat Transfer
When a temperature difference exists between two substances,
heat is transferred from one to the other by means of radiation,
conduction, or convection. Typically, several mechanisms of heat
transfer take place simultaneously.
Radiation refers to heat transfer by the emission of electromagnetic waves that carry energy away from the emitting body
and are absorbed by another body. All objects absorb and emit
energy. The rate of heat absorption depends on the properties of
the material and the geometry of the surface interacting with the
incoming radiation (see Activity 4.1). If an object’s rate of absorption of incoming energy is greater than its rate of energy emission, its temperature will rise (assuming no heat transfer mechanism other than radiation). If the rate of absorption of energy is
less than the rate of emission, the temperature of the object will
fall. An object will reach an equilibrium temperature when the
Two misconceptions should be clarified in the context of the greenhouse effect. (1) The term greenhouse is actually misleading. A greenhouse remains warm primarily because convection is
inhibited and not because of emission and absorption of longwave radiation by the air in the greenhouse (another analogy that can be used here is how hot it can get inside a car parked on a sunny
day with windows closed vs. a car parked with its windows open). (2) The greenhouse effect is not an inherently harmful phenomenon; without it, Earth would be a frigid place. Anthropogenic
effects, however, significantly increase the natural insulating properties of Earth’s atmosphere, causing Earth’s surface temperature to rise further.
1
33
(2) Water evaporating from the ocean carries latent heat
into the atmosphere. This latent heat is released when water
condenses to form clouds, warming the atmosphere. Evaporation
is also the primary reason why large lakes and the ocean are
rarely warmer than 28–30°C.
The human body takes advantage of water’s high latent heat
of vaporization. A small amount of evaporation can cool a body
substantially, which is what we experience when we perspire. The
water that evaporates from our skin gains the energy needed to
evaporate from the skin itself, which reduces our skin temperature. This phenomenon is also why you feel chilly when you get
out of the pool on a hot summer day. A common misconception is that you need to heat water to 100°C for it to evaporate,
although people are aware of hanging towels or rain puddles
that “dry” at lower temperatures. In liquids, molecules move
randomly at a variety of speeds. As a result, they bump into each
other and, in the process, some molecules gain kinetic energy
and some lose kinetic energy. For some molecules, the gained
kinetic energy is sufficient to allow them to break free of the
liquid and become gas. The molecules left behind are the slowmoving ones. Thus, the average kinetic energy of the molecules
in the liquid decreases when the fast ones “escape” and the liquid
is cooled. Heating results in higher average kinetic energy of
molecules in the liquid, and statistically more molecules gain the
needed energy to “escape” the liquid. Evaporation can even take
place directly from the solid phase (called sublimation), as we
often observe in Maine (and other similar places) during winter
when snow “disappears” even though the temperature remains
below the snow’s melting point.
Faster-vibrating molecules of a warmer object will collide with
slower-vibrating molecules of a colder object, resulting in a net
transfer of energy from the faster-vibrating molecules to the
slower ones. The rate of heat transfer by conduction is proportional to the area through which heat is flowing (with larger
areas allowing for higher transfer rates) and to the temperature
gradient (with steeper gradients causing higher transfer rates).
The rate also depends on the thermal conductivity of the materials (that is, their ability to conduct heat).
Convection and advection are the major modes of heat
transfer in the ocean and atmosphere. Convection occurs only
in fluids and involves vertical motion of fluid, or flow, rather
than interactions at the molecular level. It results from differences in densities—hence buoyancy—of fluids. Examples of
convective processes include: currents in Earth’s mantle, which
drive the tectonic system and result from heating and cooling
of magma; atmospheric circulation resulting from uneven solar
heating (e.g., between the poles and the equator); the global
ocean conveyor belt and formation of deep water masses,
resulting from cooling of surface water at high latitudes; and
vertical mixing in the ocean’s upper layer due to variations in
heating between day and night (for more details see Garrison,
2007, or any other general oceanography textbook). Advection
usually refers to horizontal transfer of heat with the flow of water
(e.g., the Gulf Stream).
Latent Heat
When an object gains heat, two things can happen: the temperature of the object can rise, or the object can change its state
without a measurable change in temperature (e.g., ice melting
into water). Most materials have two state transitions: from solid
to liquid and from liquid to gas. The heat needed to change the
state of a material is called latent heat of fusion (for changing
from solid to liquid) and latent heat of vaporization (for
changing from liquid to gas). Latent heats of fusion and vaporization for water are high (approximately 334 J/g and 2260 J/g,
respectively). These high values have many important consequences for Earth’s climate, including the following:
(1) In polar regions, as water freezes during winter, latent heat
is added to the atmosphere and surrounding liquid water. In
summer, as ice melts, heat is removed from the ocean and atmosphere. Because addition or removal of latent heat results only in
a phase change of the frozen water, not a change in its temperature, seasonal changes in ocean surface temperature (and hence
air temperature) are relatively small in these regions. Think about
ice cubes that keep a drink cold. Only after all the ice melts does
the drink’s temperature begin to rise.
Thermal Expansion
Most substances expand when heated and contract when
cooled. As the temperature of most substances increases, their
molecules vibrate faster and move farther apart, occupying a
larger space. When these substances are cooled, their molecules
vibrate slower and remain closer to each other. Note that freshwater below 4°C actually expands when cooled, a phenomena
known as the anomaly of water. Thermal expansion is the
principle by which a liquid thermometer works. In the ocean,
thermal expansion is thought to contribute significantly to sea
level rise on decadal-to-century-long time scales. However,
thermal effects appear to be influenced by decadal climaterelated fluctuations, making it difficult to estimate the long-term
contribution of thermal expansion to sea level rise (Lombard
et al., 2005). Current estimates suggest that thermal expansion is
responsible for 25% to 50% of observed sea level rise.
34
Description of Activities
We begin the lesson by asking students to define heat and
temperature, usually in small groups of three to four members
each. We then gather to discuss their definitions and review
mechanisms of heat transport (how does heat “flow”?). Then,
through hands-on/minds-on, inquiry-based activities, we
illustrate the concepts of absorption and emission of heat
(Activity 4.1), heat transfer (Activities 4.1–4.3), latent heat
(Activities 4.4 and 4.5), the relationship between evaporation and
temperature (Activity 4.6), and thermal expansion (Activities 4.7
and 4.8). During the activities and class discussion sessions, we
communicate the underlying principles of these concepts and
highlight their significance for ocean and climate processes.
Figure 4.1. Setup for Activity 4.1. The thermometers show the difference in
temperature between the black and shiny cans after the cans have been
exposed to a light source.
Activity 4.1. Radiative Heat Transfer
and Absorption of Radiation (Figure 4.1)
Materials
Explanation
•
Two cans of the same size, one black and one shiny (each can
lid should have a hole through which a thermometer can be
inserted)
• Two thermometers
• Heat lamp (we use a 150 W white bulb)
Note: A pre-made radiation kit is available at sciencekit.com.
Although the two cans are exposed to the same light source,
the two thermometers do not show the same temperature
(Figure 4.1). The shiny can reflects more radiant energy than the
black can and therefore absorbs less heat. The black can will heat
up faster. The temperatures of the cans will not rise indefinitely
but will reach a stable final temperature when the gain of shortwave radiation equals the loss of longwave radiation plus the
loss of heat to the surrounding air through conduction.
Instructions to the Students
1. You have two cans: one is shiny and the other is black. If the
same light source shines on both cans, will the temperature
inside the cans be the same? Why or why not?
2. Record the initial temperatures of the thermometers inserted
in the cans.
3. Make sure that the cans are the same distance from the light
source. Turn on the light and observe the thermometers. What
do you see? How can you explain your observations? How is
heat being transferred in this system?
4. If you keep the light on for a very long time, will the temperature continue to increase as long as the light is on? Why or
why not? By what mechanism(s) is heat being transferred in
this system?
5. How do you think principles learned from this activity apply
to absorption of electromagnetic radiation at Earth’s surface
and the regulation of Earth’s temperature?
Activity 4.2. Conduction (Figure 4.2)
Materials
•
Three types of material at room temperature: wood,
metal, and cloth
Instructions to the Students
1. All three materials have been at room temperature for quite
a while. Without touching the objects, predict their temperatures. Will they all feel the same or different with respect to
temperature? Why or why not?
2. Briefly place your hand on each material. Does it match your
expectations? How would you explain your observations given
that all items have been at room temperature?
3. What do your observations reveal about the sensing of
temperature by the human nervous system (and that of
other organisms)?
4. When and where do you think conduction comes into play in
the ocean?
This activity could be modified (e.g., to serve as an assessment
tool) to include a can with water in it vs. one without or by using
a fan to enhance convection. (Be careful that water does not
touch the heat lamp.)
35
3. Place the right column in the hot-water container and place
the left column in the ice-water container. Add a few drops
of dye to the two columns (different color to each column)
and observe whether the water circulation agrees with
your prediction.
4. What if you warm (or cool) only one column of the apparatus?
Try it.
5. What ocean and atmosphere processes can be demonstrated
using this activity?
Figure 4.2. Materials for Activity 4.2.
Explanation
Explanation
When one column of the apparatus is warmed and the other
is cooled, density differences are created between the bottom
of the vertical tubes, causing a pressure gradient to develop.
Density differences cause water masses to sink or rise until they
reach their density equilibrium level; once a water mass reaches
its equilibrium density level, it begins to move horizontally
in response to a pressure gradient. (Note: Pressure gradients
result from differences in the vertical distributions of density,
and hence hydrostatic pressure, between regions where water is
denser or lighter.) Because the cold water is denser, it will move
along the lower connecting tube; the hot water will move along
the upper connecting tube (Figure 4.3). If you cool or warm
only one column, you will see the same effect though it may
not appear as dramatic because the pressure gradients will be
smaller. This activity provides a good illustration of densitydriven ocean circulation—for example, the global conveyor belt.
It is important, as with any demonstration, to draw students’
attention to where an analogy breaks down so misconceptions
You experience heat transfer by conduction whenever you
touch something that is hotter or colder than your skin. Roomtemperature materials that are good conductors (e.g., a piece
of metal) feel colder to the touch because heat is transferred
away quickly, keeping the area we touch from heating up to
our body’s temperature. Poor conductors (e.g., a piece of cloth)
heat locally and thus feel warmer because heat transfer away
from our hands is slower. Solids, in general, are better conductors than liquids, and liquids are better conductors than gases.
Metals are very good conductors of heat, while air and blubber
(fat) are very poor conductors. A tile floor feels colder than a
carpeted floor even though both are at room temperature. Tile
is a better heat conductor than wool, so heat is transferred away
from your bare feet faster on tile than on a rug. Conduction is
not a dominant process of heat transfer in the ocean. However,
conduction always occurs at the interface between materials
of different properties (e.g., liquid and solids, as in the case of
marine organisms and the surrounding water; and liquid and
gas, as in the case of the ocean and the atmosphere).
Activity 4.3. Convection (Figure 4.3)
Materials
•
Convection setup (homemade or from sciencekit.com)
Food coloring (two colors)
• Container with ice-cold water
• Container with hot water
•
Instructions to the Students
1. Fill the apparatus with water. (Make sure no bubbles are in the
horizontal tubes.)
2. If you warm the right column and cool the left column, what
direction would you expect water to flow through the horizontal tubes?
Figure 4.3. Convection apparatus. Note the warm water (red) flows at the
top and the cold water (blue) at the bottom due to the difference in density
between the fluids on opposite sides.
36
do not arise. For example, the global conveyor belt results from
cooling at the water surface, while in this demonstration cooling
and heating are done from the bottom (the atmosphere, on the
other hand, is heated from below so atmospheric buoyancydriven circulation is a better analogy). This activity can be also
used in conjunction with Chapter 1.
Activity 4.4. Heat Pack (Figure 4.4)
Materials
•
Two containers with water
Reusable heat pack (from Arbor Scientific) at room
temperature
• Two thermometers
• Watch or stopwatch
Note: We usually do this activity as a class demonstration. If you
intend to use this activity with multiple groups, you will need to
obtain several heat packs (which are inexpensive). Once a pack
is activated and the material in it solidifies, you will need to heat
it for about 20 minutes to return it to the liquid phase.
•
Figure 4.4. Materials for Activity 4.4.
sodium acetate. When the pack is activated, a nucleation center
is formed and the sodium acetate begins to crystallize, releasing
stored energy as heat. The released heat is being conducted from
the pack to the water, and fluid motions (convection and advection) distribute the heat within the water in the container. To
return the pack’s contents to the liquid phase, you will need to
heat the pack (i.e., “invest” energy). This activity demonstrates
the heat release that accompanies a phase change and can be
discussed in class in the context of latent heat released during
ice formation and cloud condensation.
Instructions to the Students
1. Observe, feel, and describe the heat pack (e.g., material and
temperature).
2. Fill the containers with room-temperature water and record
the initial temperature of each.
3. Activate the heat pack by pressing the button (use the ball of
your fingers—don’t use your nails, as they might damage the
pack) and add it to one of the containers. The other container
serves as a control.
4. Immediately record the starting temperature in both
containers.
5. Continue recording the temperature in each container, once
every minute for 10 minutes.
6. Did you observe differences in the water temperature between
the two treatments? What causes the change in water temperature? How does this pack work? (Hint: Did the material in the
pack look the same before and after you activated the pack?)
7. What processes in the ocean and atmosphere are analogous to
what you just observed in this activity (a phase change followed
by a change of temperature in the surrounding waters)?
Activity 4.5. Heat Flow and Latent
Heat (Figure 4.5)
Materials
•
•
•
•
•
A small plastic container with a top. The container should be
small enough to fit inside a Styrofoam cup. Drill a hole in the
top of the container, large enough to fit a thermometer.
Styrofoam cup(s). Nest several cups within each other for
better insulation. Mark the cup with a line to indicate the
volume of water that needs to be added so that the volume
of water in the plastic container is the same as the volume of
water in the Styrofoam cup.
Two digital thermometers
Ring stand with a clamp and platform
Hot tap water, ice-cold water, and ice
Explanation
Instructions to the Students
When an activated heat pack is placed in water, the water
temperature begins to rise. In contrast, water temperature in
the control container (without the heat pack) remains constant.
The heat pack contains a supersaturated aqueous solution of
1. Draw a cartoon of the experimental setup (Figure 4.5) and
using arrows indicate the direction of heat transfer if the small
plastic container contained ice-cold water (with no ice) and
37
the Styrofoam cup contained hot water. What would happen
to the temperature of the water in the small plastic container?
What would happen to the temperature of the water in the
Styrofoam cup?
2. Fill the small plastic container to the top with ice-cold water
(no ice!). Record the initial temperature of the water in the
container. Affix this container to the clamp.
3. Fill the Styrofoam cup with hot tap water to the marked line
(so the volume of water in the container equals the volume of
water in the cup). Record the initial temperature of the water
in the cup.
4. Slide the arm of the clamp down and place the small container
inside the cup so that it is immersed in the hot water. Record
the temperature in the container and the cup every 30 seconds
for four minutes. Using the rod of the thermometer, mix the
water in the cup and the container while doing the measurements to eliminate any temperature gradients that might be
developing. (In other words, don’t allow light, warm water to
accumulate and float on top of cold, denser water.)
5. Plot the temperature in the container and the cup as a function of time. Do your observations agree with your prediction?
What do you expect the temperature gradient to be after a
longer period of time?
6. Assume that you repeat the experiment, but this time you fill
the small plastic container with ice + water and fill the cup
with hot tap water (don’t do it yet!). Do you expect to see
similar changes in temperature in this setup? Why or why not?
7. Fill the small container to the top with ice and water (approximately 60% ice and 40% water). Record the initial temperature
of the water in the container.
8. Repeat Steps 4 and 5. Do you see the same trend as you saw in
Step 5? Why or why not?
Explanation
Heat is transferred through conduction from a high-temperature substance to a lower-temperature one. In this experiment,
heat is transferred from the hot water in the Styrofoam cup to
the cold water in the plastic container in the middle of the cup.
As a result, the temperature of the water in the cup decreases
(heat is removed) while the temperature in the inner plastic
container increases (heat is gained). After a long period of time,
the system will reach equilibrium, and there will be no temperature gradient between the water in the Styrofoam cup and the
water in the container. When ice + water is added to the plastic
container and hot water is added to the cup, heat transfer is in
the same direction as before—but now, while the temperature
of the hot water decreases, there is no observed change in the
temperature of the water + ice (because heat is invested in
melting the ice). Only after all the ice melts will the temperature
of the water in the plastic container begin to rise.
Activity 4.6. Sling Psychrometer
(Hygrometer) (Figure 4.6)
Materials
•
Sling psychrometer (sciencekit.com)
Instructions to the Students
1. A sling psychrometer is a device that allows us to measure
relative humidity by comparing the temperature of a thermometer wrapped in a wet cloth (the wet bulb) with the
temperature of a dry bulb. How do you expect the temperature between the two thermometers to vary as a function
of humidity? Why might there be a difference between
the two readings?
2. Swing the psychrometer for 20 seconds and then note if
there is any difference in temperature between the two thermometers. (We ask students to take at least three readings
and find the median. We use these data later for a discussion
on measurements).
After the activity, have the students discuss the concept
of humidity and describe the expected relationships among
humidity (mugginess), evaporation, and ambient temperature.
Figure 4.5. Setup for Activity 4.5.
38
Instructions to the Students
1. Fill the bottle with colored water. Push the stopper down
until the fluid rises one-third the length of the tube above the
stopper. Mark the water level with tape.
2. What do you expect will happen to the water level in the tube
when you place the flask in a container with hot water? Why?
3. Place the flask in a container filled with hot water. Observe the
water level in the glass tube for at least three minutes. Mark
the new water level. Does it agree with your prediction?
4. Apply what you have learned in this activity to predict and
explain what will happen to the ocean’s volume if ocean waters
become warmer. What would be the implications for sea level?
5. What other processes influence sea level? Challenge: Would
the melting of land-based ice and sea ice have the same
effects on sea level? Why or why not? How would you test
your prediction?
Figure 4.6. A sling psychrometer and its conversion table.
Following this discussion, students should be able to explain
(possibly as an assessment) how one could use the psychrometer
to determine humidity at a given ambient temperature (as is done
with a table provided by the manufacturer; Figure 4.6).
Explanation
When a fluid is heated, it usually expands; when cooled, it
usually contracts (with some important exceptions, e.g., H2O
below 4°C). This is the principle by which a mercury or ethanol
thermometer operates. Increased heating of the ocean due
to global warming will result in seawater expansion, and the
increase of water volume in ocean basins will cause sea level to
rise. Other processes contributing to sea level change include
the addition of water from the melting of glaciers and land ice
caps, and the rise and fall of lithospheric plates due to isostatic
Explanation
The sling psychrometer consists of two thermometers mounted
together. One is a regular thermometer; the other is a wet-bulb
thermometer (which has a wet cloth “sock” over the bulb).
When you whirl the instrument, water evaporates from the
wet cloth (in contact with fresh air), cooling the wet-bulb thermometer. The temperature of the wet bulb reaches equilibrium
when cooling due to evaporation of the fluid (which depends
on the relative humidity in the room) is in equilibrium with
the gain of heat through conduction from the surrounding air.
If the surrounding air is dry, evaporation will be high, and the
difference in temperatures between the two thermometers will
be greater. If the air is saturated with water vapor, no evaporative cooling will take place, and there will be no difference in
temperature between the two thermometers.
Activity 4.7. Thermal Expansion
(Figure 4.7)
Materials
•
•
•
•
•
•
Flask
One-hole stopper
Long glass tube
Container filled with hot water
Food coloring
Lab tape
Figure 4.7. Setup of Activity 4.7 following the flask’s
immersion in hot water.
39
leveling. Melting of sea ice does not change sea level because
the volume of water displaced by an iceberg equals the volume
added when it melts. To demonstrate this concept, ask the
students to place a large block of ice in an aquarium and record
the water level before and after the ice melts. Note: Some “sea
level” change may be observed if the ice cools the water enough
to cause significant contraction.
Activity 4.8. Reversing Rods (Figure 4.8)
Materials
•
•
•
•
•
Two glass beakers: one filled with cooled water (below 20°C)
and one filled with warm water (~ 40°C)
A set of reverse density rods: one aluminum rod, one plastic
rod (from Arbor Scientific)
Thermometer
Ice (may be needed to cool water)
Hot plate (optional; hot tap water will work fine)
Figure 4.8. Aluminum and plastic rods immersed in cold and warm water.
place the rods in hot water, the density of the water is now
lower than that of the aluminum rod, and the rod sinks. The
PVC rod is also initially denser than the water and it sinks too,
but it expands significantly as it warms. As a result, its density
decreases (again, its mass remains constant, but its volume
increases). When its density becomes lower than that of the
water, it floats. This activity can be also used in Chapter 1.
Instructions to the Students
1. What will happen to the rods (float/sink) if you place them in
a beaker with cold water? What is the reasoning behind your
prediction?
2. Place the rods in the beaker with cold water. Make sure no air
bubbles are attached to the rods.
3. Does your observation agree with your predictions? Observe
the rods for at least five minutes.
4. Repeat this experiment, this time using the beaker filled with
hot water. Observe the rods for at least three minutes. What is
happening?
5. How would you explain the different behaviors of the rods in
cold vs. warm water? With your group, discuss possible explanations for what you have observed.
Supplementary activity
We have noticed that many students confuse the time of the
day at which solar radiation is maximal (around noon) with the
time of the day at which the temperature is maximal (several
hours later in the afternoon). Similarly, students confuse the
shortest or longest day of the year, when incoming solar flux is
close to minimal or maximal values, with the time of year when
air temperature or water temperature in the ocean and in lakes
are (on average) the coldest or warmest (ignoring nonradiative
processes that affect water temperature, such as upwelling).
This issue stems from confusion about temperature versus the
rate of change of temperature. The rate of change of temperature
is proportional to the heat flux (when no phase transition takes
place). As a class activity, we ask students to draw a qualitative cartoon of what they think a plot of water temperature vs.
time of year would look like. We then ask them to go to the
GOMOOS Web site (http://www.gomoos.org/gnd/ or any other
Web site that provides real-time sea surface temperature) to plot
the annual sea surface temperature (weekly or daily averages)
vs. time, and to observe when the water or air temperature is
maximal. (This activity can be done as a homework assignment.) In class, we discuss the difference between temperature
and the rate of change of temperature that is associated with the
heat flux. For example, the radiative heat flux in Maine (hence,
Explanation
In this activity, one rod is made of aluminum and the other
of PVC. When you place the rods in cold water, both initially
float because their densities are lower than that of the cold
water. Over time, the PVC rod gets colder and contracts, which
results in a density change. (Its volume decreases, but its mass
remains the same.) When the density of the rod exceeds that
of the water, the PVC sinks. The aluminum rod gets colder
too, but aluminum expands and contracts much less than PVC
when its temperature is changed by the same amount (that is,
it has a smaller “thermal expansion coefficient”). Therefore,
the aluminum rod’s density is less affected by the temperature
change, and the aluminum rod remains floating. When you
40
the rate of change of temperature) is, on average, lowest in
December and highest in June (associated with the shortest and
longest days of the year). The ocean and atmosphere, however,
continue to lose heat after December (or gain heat after June),
even though the radiative heat flux is not at its minimal (or
maximal) value. Thus, the water temperature continues to drop
after December and continues to rise after June. The temperature will stop changing (reaching a maximum or minimum
value) when the heat gain equals the heat loss. In the Gulf of
Maine, maximum average sea surface temperature occurs in
September, not June. A similar argument can be presented to
explain why the hottest period during a day is not noon, when
the flux of incoming solar radiation is close to its maximal
value, but a few hours later. An analogy some students are
familiar with is the time lag between the maximal acceleration
of a car when they floor the gas pedal and when the car speed
is maximal (which occurs later, when acceleration processes
and deceleration processes are equal). Acceleration (time rate
of change of velocity) is the analogue for heat flux (proportional to the time rate of change of temperature, assuming
no phase transitions).
References
Carlton, K. 2000. Teaching about heat and temperature. Physics Education
35:101–105.
Garrison, T.S. 2007. Oceanography: An Invitation to Marine Science, 6th ed.
Thomson Brooks/Cole, 608 pp.
Gill, A.E. 1982. Atmosphere-Ocean Dynamics. Academic Press, 662 pp.
Hewitt, P.G. 2008. Chapters 8 and 9 in Conceptual Physics Fundamentals. Pearson
Addison-Wesley.
Lombard, A., A. Cazenave, P.Y. Le Traon, and M. Ishii. 2005. Contribution of
thermal expansion to present-day sea level rise revisited. Global and Planetary
Change 47:1–16.
Thomaz, M.F., I.M. Malaquias, M.C. Valente, and M.J. Antunes. 1995. An attempt
to overcome alternative conceptions related to heat and temperature. Physics
Education 30:19–26.
Other Resources
Sorbjan, Z. 1996. Hands-On Meteorology: Stories, Theories, and Simple Experiments.
American Meteorological Society, Washington, DC. A collection of hands-on
experiments designed around concepts of meteorology. Chapter 4 addresses
heat. In addition to the experiments, the book contains historical narratives, references to important discoveries, and stories about famous and
infamous scientists.
http://cosee.umaine.edu/cfuser/index.cfm. The COSEE-OS ocean-climate Web
interface provides images, videos, news items, and resources associated with
ocean heat storage, sea surface temperature, convective and advective heat transport processes, climate warming, and the greenhouse effect.
41
Team-Based Learning
Team-based learning, also referred to as cooperative learning,
is a pedagogical approach in which students work in small
groups to achieve learning goals. It provides students with
opportunities to converse with peers, brainstorm, present
and defend ideas, and question conceptual frameworks.
In this approach, the instructor acts as a facilitator and
content expert rather than a lecturer. Team-based learning
can develop problem-solving, communication, and criticalthinking skills. In addition, it can increase students’ selfesteem and their ability to work with others, as well as
improve their attitudes toward learning (Slavin, 1981). Much
has been written about this strategy, including a book we
recommend on cooperative learning, written by an oceanographer (McManus, 2005). The University of Oklahoma Web
site on team-based learning contains a wealth of information
(http://teambasedlearning.apsc.ubc.ca/). Our goal here is to
highlight key elements of cooperative learning, as this strategy
integrates well with the inquiry-based teaching and learning
approach we advocate.
Team-based learning can be used in the classroom or lab or
outside the classroom to help students complete class assignments. It can take many different forms (e.g., Hassard, 2005;
Joyce and Weil, 2009). Examples include:
• Think-pair-share. Students are asked to first think about a
question or a problem independently and then discuss their
ideas with the student sitting next to them. Each pair then
shares their ideas with the class.
• Roundtable or circle of knowledge. A group of three or more
students brainstorm on an assigned problem and record
their ideas. Each group then presents its ideas to the class.
• Jigsaw. In teams, each student is assigned to research one
aspect of the learning assignment. Students then teach their
topic to their team members. Students assigned the same
topics can form “expert groups” to brainstorm and discuss
their topic before presenting it to their own teams.
• Constructive controversy. Teams or pairs of students are
assigned opposing sides of an issue. Each team researches,
prepares, and presents its argument. The class discusses the
issue after all teams have presented.
42
Essential Elements
Regardless of the specific strategy used for team-based
learning, several essential elements are required for this
approach to be successful. First, the instructor must promote
individual and group accountability for learning, making sure
that group time is, indeed, used for achieving group learning
goals and not for social conversation. Second, the instructor
must achieve interdependence among the students in the
learning teams, and the students must know that a “chauffeur/hitchhiker” situation is unacceptable. Teammates must
know that the team’s success depends on individual learning
by each team member and must feel that they need each
other in order to complete the group’s task (i.e., they “sink
or swim” together). These first two elements can be achieved
by dividing tasks, assigning roles, providing feedback, and
assessing individual learning outcomes. To avoid a “chauffeur/hitchhiker” situation, team members can be randomly
assigned to take leading roles and to represent their groups
during class discussions.
Another important element is that students must learn and
develop cooperative skills. Skills include those for working
together effectively (e.g., active listening, staying on task,
summarizing, recording ideas) as well as maintaining group
“spirit” skills (e.g., encouraging each other, providing feedback). Finally, students should be given the opportunity to
reflect on how well they work as a team. The determination of
how well groups are functioning and how well they are using
collaborative skills can be assessed on an individual, teamwide, or whole-class basis.
Our experience is that students who have not previously
been involved in cooperative learning do not initially like this
approach because they are concerned that their grades will be
affected by other team members. We tell students, therefore,
that peer evaluation of the group’s project and functionality
will contribute a certain fraction to the final grade. The team’s
peer evaluation is done by each team member individually, and
students are assured that their evaluations will not be shared
with other team members. Students are prompted to evaluate
how well the team collaborated, using questions (e.g., Angelo
and Cross, 1993) such as:
•
How well did your group work together on this assignment?
• How many of the group members participated actively most
of the time?
• How many of the group members were fully prepared for
the group work most of the time?
• Give one specific example of something you learned from
the group that you probably wouldn’t have learned working
alone.
• Give one specific example of something the other group
members learned from you that they probably wouldn’t have
learned otherwise.
Each student is also asked to provide a self-evaluation,
through questions such as:
• How comfortable did you feel working with the group?
• Were you an active participant?
• How well did you listen to team members?
• To what degree did you help other team members to better
understand the material?
• Did you ask for help from a team member when you did not
understand an idea or concept?
Finally, each student is asked to evaluate the percent contribution (out of 100%) of each team member, except self, to
the assignment and provide an explanation for the evaluation. Information on grading formulas for peer evaluations
can be found on the Team Based Learning Web site: http://
teambasedlearning.apsc.ubc.ca/?page_id=176.
Teams can be formed by the students (self-selection) or by
the instructor (randomly or purposefully). Self-selected and
randomly assigned teams can result in groups that are not
heterogeneous and/or not equal in ability. As a rule, groups
should stay together long enough to feel successful as a group,
but not so long that team dynamics become counterproductive (e.g., when team members settle into fixed roles). Group
size may also vary. In smaller groups, each member generally
participates more, fewer social skills are needed, and groups
can work more quickly. In larger groups, more ideas are generated and a smaller number of group reports is produced.
It is not enough to simply tell students to work together.
Incentives and a healthy sense of competition can enhance
students’ motivation, engagement, and contributions to the
team. Reward structures may be based on team points (the
team with the most points wins), on criterion achievement
(any team reaching a predetermined criterion, such as all
team members scoring 85% or better, receives a reward), or
on team improvement (students contribute to their teams
by improving over their past performances). In the teamimprovement case, high, average, and low achievers are
equally challenged to do their best, and the contributions of all
team members are valued.
References
Angelo, T.A., and K.P. Cross. 1993. Classroom Assessment Techniques:
A Handbook for College Teachers, 2nd ed. Jossey-Bass, San Francisco,
CA, 448 pp.
Hassard, J. 2005. The Art of Teaching Science. Oxford University Press, 476 pp.
Joyce, B.R., and M. Weil. 2009. Models of Teaching, 8th ed. Allyn and Bacon,
576 pp.
Michaelsen, L.K., and R.H. Black. 1994. Building learning teams: The key to
harnessing the power of small groups in higher education. Pp. 65–81 in
Collaborative Learning: A Sourcebook for Higher Education, vol. 2. S. Kadel
and J. Keehner, eds, National Center on Postsecondary Teaching, Learning,
& Assessment, University Park, PA.
McManus, D.A. 2005. Leaving the Lectern: Cooperative Learning and the Critical
First Days of Students Working in Groups. Anker Publishing Company Inc.,
210 pp.
Slavin, R.E. 1981. Synthesis of research on cooperative learning. Educational
Leadership 38(8):655–660.
43
Chapter 5. GRAVITY WAVES
Activity 5.1. Wave Speed and
Water Depth (Figure 5.1)
Purpose of activities
The purpose of these activities are to familiarize students with
wave motion in general and gravity waves in particular. Concepts
such as resonance, natural frequency, and seiche are demonstrated. Other topics that are emphasized during class discussion
are measurements and their statistics, and dimensional analysis.
Materials
•
Rectangular tanks marked at 1.5 cm above the bottom and
6 cm above the bottom (from sciencekit.com)
• Stopwatches
• Container with water
BACKGROUND
Procedure and Explanation
Waves are ubiquitous in the ocean and in lakes; surface gravity
waves, in particular, are a common sight at beaches. Gravity
waves are important in a variety of oceanic processes, including
the passage of momentum from wind to the ocean, mixing
enhancement through wave breaking, beach erosion, and
accumulation of floating debris at beaches. Their importance in
recreation and popular culture (surfing) and their destructive
powers (tsunamis) make them familiar even to students living
inland. However, such waves are seldom used to teach about
harmonic motions at the college and high school levels.
We first ask students to suggest what characteristics may affect
the speed of a small-amplitude wave (by small we mean that its
height << wavelength). Quantities usually suggested are gravity
(g, gravitational acceleration [the restoring force]; dimension
L/T2), wavelength (λ; dimension L), depth (H; dimension L),
and density (ρ; dimension ML3). From dimensional analysis
alone (Box 5.1), we come up with the wave propagation speed
being proportional to gH or g λ times any function of H/λ.
Generally speaking, waves with a wavelength smaller than the
depth over which they travel (i.e., deep water waves, λ << H) do
not interact with the bottom, and their velocity is dependent on
the wavelength (termed “dispersive” waves). Waves with a wavelength larger than the depth over which they travel (i.e., shallow
water waves, λ >> H) do interact with the bottom, and we expect
the depth to be a factor in their propagation (these are “nondispersive” waves). Longer-wavelength waves penetrate deeper (the
depth of wave penetration and the decrease of its amplitude
DESCRIPTION OF Activities
We start the lesson by asking the students to describe waves they
are familiar with and that are associated with the ocean. Most
are familiar with surface gravity waves, tsunamis, sound, and
light. We use a Slinky to demonstrate differences between transverse and longitudinal waves (e.g., Hewitt, 2008). We discuss
wave descriptors such as wavelength, frequency, amplitude,
period, propagation (or phase) speed, and the direction of movement of particles in the medium. We discuss what is carried by
waves (energy, information) versus what is not (components of
the medium; e.g., a piece of foam bobs up and down as waves
pass but doesn’t propagate significantly with them over a wave
period). As an analogy, we give the example of a stadiumaudience wave that is achieved when spectators stand and raise
their hands in sequence. The wave travels through the crowd,
and it is easy to see how information is transferred while the
spectators remain in place in their seats. Time could be saved
by providing reading materials prior to class (e.g., Chapter 13 of
Denny, 1993), familiarizing students with waves and allowing for
in-class exploration of additional topics such as capillary waves
and internal waves. The following activities are presented as a
sequence that the class follows collectively, with students seated
in small groups of three to four members to facilitate discussion.
Figure 5.1. Wave speed and wave depth. Students measure the number of
“sloshes” in a tank filled with water to a depth of 1.5 cm.
44
Box 5.1. Dimensional analysis
Dimensional analysis is a powerful technique used to explore likely relationships between an observed phenomenon and the
physical variables associated with it. Most physical quantities can be expressed in terms of some combination of five dimensions: length (L), mass (M), time (T), electrical current (I), and temperature (t).
For example, let’s say that we would like to know what physical attributes determine the period of a swing. The physical
characteristics of the swing are its mass (m, [M]) and the length of the rope (l, [L]). The restoring force acting on it is gravity
(associated with the gravitational acceleration g [L/T 2 ]). How can we use all of these variables to obtain the dimension of time
associated with the period of the swing? The only combination that provides this dimension is l /g . Surprisingly (to some),
this simple analysis suggests that the mass of the swing plays no role. These results can easily be verified empirically.
Dimensional analyses have been very useful in fluid dynamics in general and in geophysical fluid dynamics in particular,
given the complexity and nonlinearity of the ruling mathematical descriptions. Use of dimensions and scaling helps to simplify
equations (by “scaling out” terms) to study a given phenomenon.
from surface to depth both scale with its wavelength). The wave
is at the interface, but motion associated with the wave is felt at
depth. To test whether wave velocity is dependent on the fluid’s
depth, we do the following activity.
Each group of students receives a small rectangular tank
(L = 30-cm long). The tanks are filled with water 1.5-cm deep.
Students are asked to create a wave by lifting one side of the tank
off the table, then setting it back down, and to record the number
of times the disturbance bounces back and forth from the walls
in a time interval of 5 s (there are ~ 6 sloshes during this period;
Figure 5.1). Students are then asked to figure out how to turn
this information into a measure of velocity (length of tank
times sloshes per unit time = 30 cm x 6/5 s ≈ 0.36 m/s vs. the
velocity calculated from dimensional analysis: gH = 0.38 m/s).
Expected uncertainties are on the order of 10–20% (given reaction time and accuracy of locating the position of perturbation at the end). The tanks are then filled to a depth of 6 cm.
Repeating the measurements of wave propagation indeed shows
that the wave bounces about 12 times in 5 s (velocity ≈ 0.72 m/s
vs. the velocity calculated from dimensional analysis:
gH = 0.76 m/s). Note that no dependence on the initial wave
amplitude (variable between groups) is observed. The wave in
the tank has a wavelength of 60 cm (λ >> H). We discuss the
fact that if the theoretical prediction is correct (dependence
on H ), quadrupling the depth should double the wave
velocity and hence the distance traveled in 5 s (as is observed).
If multiple groups participate or if replications are done,
statistical descriptors of the results, such as mean and median
speeds and measures of variance and their uncertainties, can be
introduced and computed.
At this stage, we ask the students whether a tsunami is a deep
or shallow water wave. Because a tsunami’s lateral extent is
determined by the length of the fault zone ruptured during the
earthquake (~ 100,000 m) and the maximal depth of the ocean
is significantly smaller (~ 11,000 m), it qualifies as a shallow
water wave. Then, why is it so destructive? Given that speed is
depth-dependent (~ H ), surface gravity waves slow down as
bathymetry shoals and wavelength shortens. That is, the “front”
of the shallow water wave propagates slower than its “back” when
depth decreases. Wave shoaling increases the wave’s steepness
(as trough and crest get closer), causing the wave to eventually
break. In the open ocean, a tsunami might have a speed of several
hundred kilometers per hour and a height of only a few centimeters, but as the wave approaches shore, its speed slows and its
height increases significantly, sometimes up to many meters.
The slowing of waves in shallow water also causes wave refraction when waves arrive at a beach at an angle. Wave refraction,
well known to some from Snell’s Law, refers to the change of
wave front directions due to a change in propagation speed. As
a wave approaches the shore at an angle and “feels” the seafloor,
45
the “wave train” in shallow depth slows compared to the part at
deeper depth, causing it to align more closely with bathymetric
contours. Many good images of wave refraction can be found on
the Web by using Google Image Search.
In the ocean, breaking internal waves are responsible for mixing
of heat and nutrients at the base of the mixed layer and in the
vicinity of steep topography (e.g., Kunze and Llewellyn Smith,
2003). Internal waves can also uplift waters from darkness to a
sunlit position closer to the surface where phytoplankton populations may get sufficient light for growth. For the same excitation energy and wavelength, the amplitude of internal gravity
waves is significantly larger than that of surface gravity waves,
because the gravitational restoring force (and potential energy
associated with these waves) for a given wave height is smaller
for internal waves, given the small density contrast between the
layers of water as compared to that of water and air for surface
gravity waves. (For an alternative illustration of internal waves,
see Franks and Franks, 2009.)
At this stage, we introduce the concepts of seiche and resonance. When we perturbed the two-layer system by lifting the
tank divider, many waves were initially excited. But only those
that fit (resonate) with the geometry of the basin remain. We end
up with a single wave that propagates back and forth in the tank
with a specific rhythm. Similar to a musical instrument where a
different primary tone is produced for a given size of string or air
chamber, the geometry of a water basin (e.g., the experimental
tank, a lake, or a bay) determines which waves are excited when
forcing is applied and then released (e.g., due to a storm passage).
These waves are the “natural” modes of the basin and are termed
“seiche”; their frequency is described as the “natural” frequency.
Forcing a tank at its natural frequency excites these waves, a
phenomenon termed “resonance.” To demonstrate resonance, we
use a wave paddle (a wide piece of plastic about 2-cm high, with a
width similar to that of the tank; Figure 5.2). We lower and raise
the paddle in a stratified tank at a period matching the period
of the waves excited earlier. That is, when we apply short-period
forcing (i.e., lowering and raising the paddle at a frequency
of ~ 1 s), surface gravity waves are formed (beware of spilling).
When a longer period of forcing is applied (i.e., lowering and
raising the paddle at a frequency of ~ 10 s), internal waves are
formed. A piece of plastic inserted at an angle at one end of the
tank will simulate shallowing topography, allowing the observation of breaking internal waves (Figure 5.2).
Activity 5.2. Internal Waves (Figure 5.2)
Materials
•
Rectangular tanks with a divider (from sciencekit.com)
• Stopwatches
• Two containers: one with freshwater and the other with
dyed salty (or sugary) water (approximately 75 g kosher salt
dissolved in 1 L tap water)
Procedure and Explanation
The same rectangular tanks are used to demonstrate and discuss
internal waves that form at the interface of fluids of different
densities (e.g., stratified layers in the ocean; see Activity 1.4). The
tanks can be separated into two compartments by inserting a
plastic divider. Students are asked to fill one compartment with
freshwater and the other with salty (or sugary) dyed water, and
they are asked to predict what will happen when the barrier is
removed (see also Activity 1.4). The barrier is then removed, and
the denser fluid flows under the less-dense fluid. Once the fluid
from each compartment reaches the opposite end of the tank,
an internal wave propagates back and forth along the interface
between the two differently colored fluids (Figure 5.2). Students
are asked to measure the wave’s speed, which is significantly
slower than both surface gravity waves they encountered earlier.
Activity 5.3. Buoyancy Oscillations
(Figure 5.3)
Materials
Figure 5.2. Internal waves. An internal wave at the interface between two fluids
of different densities (dense blue water and less-dense clear water). A wave
paddle that can be used to demonstrate resonance (see text) is shown on the
right side of the tank, and a piece of plastic that simulates shallowing topography is shown on the left side of the tank.
•
46
A tall graduated cylinder with a stratified fluid (salty water on
the bottom and freshwater on top)
in the excitation of waves. An example is the La Niña/El Niño
transition, when the trade winds are significantly weakened over
the equatorial Pacific region. This change excites Kelvin waves
that propagate from west to east along the equator, as can be
observed in remotely sensed images of the height of the ocean’s
surface (e.g., http://oceanmotion.org/html/impact/el-nino.htm).
Impacts on the ocean’s biology can be observed in remotely
sensed ocean color data/images as well (e.g., http://svs.gsfc.nasa.
gov/stories/elnino/index.html).
References
Denny, M.W. 1993. Air and Water: The Biology and Physics of Life’s Media. Princeton
University Press, Princeton, NJ, 360 pp.
Franks, P.J.S., and S.E.R. Franks. 2009. Mix it up, mix it down: Intriguing implications of ocean layering. Oceanography 22(1):228–233. Available online at: http://
tos.org/hands-on/index.html (accessed August 4, 2009).
Gill, A.E. 1982. Atmosphere-Ocean Dynamics. Academic Press, Orlando, FL, 662 pp.
Hewitt, P.G. 2008. Chapter 12 in Conceptual Physics Fundamentals. Pearson
Addison-Wesley.
Kunze, E., and S.G. Llewellyn Smith. 2003. The role of small-scale topography in
turbulent mixing of the global ocean. Oceanography 17(1):55–64. Available
online at: http://www.tos.org/oceanography/issues/issue_archive/17_1.html
(accessed August 13, 2009).
LeBlond, P.H., and L.A. Mysak. 1978. Waves in the Ocean. Elsevier Oceanography
Series, 20. Elsevier, Amsterdam, 602 pp.
Lighthill, J. 1978. Waves in Fluids. Cambridge University Press, 504 pp.
Figure 5.3. Buoyancy oscillations. An object of intermediate density rests
between layers of dense bottom fluid and less-dense top fluid. If pushed down,
the object will oscillate with a frequency dependent on the difference between
fluid densities.
•
A ping-pong ball with clay attached as ballast (or a test tube
filled with washers [weights] for ballast) such that the ball (or
test tube) stays put near the interface between the two fluids.
Procedure and Explanation
Buoyancy oscillations, the highest-frequency internal waves
found in the ocean, can be easily demonstrated using a graduated cylinder and a calibrated float (Figure 5.3, left panel)
or a weighted ping-pong ball with clay attached as ballast
(Figure 5.3, right panel). Dense, salty water is introduced and
overlaid with freshwater. The float is introduced at the interface between the two layers and is perturbed by pushing it
downward with a thin rod. The oscillation’s frequency (called
the buoyancy or Brunt-Vaisalla frequency) is a function of
the contrast in density between the two layers. The frequency
is proportional to the square root of the density gradient, as
expected from dimensional analysis. Students can examine this
dependence by timing the oscillations in graduated cylinders
containing different density gradients. For advanced students,
the mathematical description of this problem can be introduced.
The mathematics is relatively simple (culminating in a onedimensional wave equation) and rewarding (e.g., Gill, 1982).
The subject of fluid waves is vast and fascinating (see, for
example, the advanced textbooks by LeBlond and Mysak, 1978,
and Lighthill, 1978). Fluids support a wide variety of waves,
spanning physics topics from surface tension, to sound, light,
and gravity waves, to vortical planetary waves (large-scale waves
with significant angular momentum, affected by Earth’s rotation).
Because waves are the information-carriers in a fluid, any change
in forcing (e.g., a change in wind patterns over the ocean) results
Additional Resources
Duxbury, A.C., A.B. Duxbury, and K.A. Sverdrup, 2000. Chapter 9 in An
Introduction to the World’s Oceans, McGraw-Hill.
Garrison, T., 2009. Chapter 9 in Essentials of Oceanography, 5th ed., Brooks/Cole
Publishing Company, Pacific Grove, CA.
Pinet, R. 2000. Chapter 7 in Invitation to Oceanography. Jones and Bartlett
Publishers Inc., Sudbury, MA.
Pond, S., and G.L. Pickard, 1983. Chapter 12 in Introductory Dynamical
Oceanography. Pergamon Press.
Thurman, H.V. 1997. Chapter 9 in Introductory Oceanography. Prentice Hall.
Waves, Tides and Shallow-water Processes. The Open University, Pergamon Press.
Movies of internal waves in continuously stratified fluids: http://www.gfd-dennou.
org/library/gfd_exp/exp_e/exp/iw/index.htm
Movies of shear-induced breaking internal waves (Kelvin-Helmholz instability):
http://www.gfd-dennou.org/library/gfd_exp/exp_e/exp/kh/1/res.htm
47
48
Acknowledgements
Our approach to teaching science arose and was nurtured by
a collaborative effort involving scientists, education experts,
and science teachers whom we have worked with through the
years. As with any other interdisciplinary collaboration, it took
time and persistence to establish a well-integrated, collaborative
teaching effort. It required us to open ourselves to unfamiliar
professional cultures and to acquaint ourselves with unfamiliar
terms. The countless benefits for our students and us, however,
definitely made it worth the effort. We thank the National Science
Foundation COSEE program for facilitating and supporting this
collaboration and for funding this supplement to Oceanography.
We also thank all the students and teachers who took part in the
development of these activities and provided helpful feedback.
We thank Annette deCharon for her support and encouragement
and to John Thompson for inspiring discussions. We are grateful
to Sharon Franks, Robert Feller, and Tonya Clayton for thorough
reviews and excellent comments that greatly improved the manuscript. Finally, publication of this document would not have been
possible without Ellen Kappel’s support and enthusiasm. We thank
her and Vicky Cullen for the dedicated and outstanding editing
job, and Johanna Adams for the layout and design.
—Lee Karp-Boss, Emmanuel Boss, Herman Weller,
James Loftin, and Jennifer Albright
www.tos.org/hands-on
August 2009